Sorry it took me a while to answer; I was working on the answer and also got busy and didn't have time to get back to the computer. Aggression cases take thoughtful answers and thus, they take some time to think about. The other trouble with answers to aggression cases is that it is best to get a professional trainer to come to your home to actually witness the problem. A recommended trainer is one that uses positive reinforcement training and not aversive training and also one who has experience in aggression cases. To find a trainer in your area go to http://www.personalizeddogtraining.com/ and click on the Puppy Manners button and then in the index, click on Find a Trainer and that will take you to links where you can search for a trainer by your zip code.
You first ask, "Will my two dogs ever get along?" The quick and dirty answer is "no" unless a lot of work and management are done. There is no quick or magic fix to the problem of resource-guarding - while working with the gradual desensitization and counter-conditioning methods helps, still a lot of owner diligence and management is needed. The reason that resource-guarding is so difficult to resolve is that it is basically what is called a "hard-wired" behavior. That is, it is tightly coupled to canine evolutionary history - in other words, it's a natural (normal) behavior. Just because it is natural or normal does not mean that that's what we want to be happening in our house or yard, however. As you have found out, what does not work is yelling NO or any of the punishment-based methods. Aversive training methods can actually make the problem worse. Another thing that people have tried that tends to not work is to satiate (overload) the environment with the food or toys that the dogs guard. This just does not work because the dogs tend to pick one of the toys and treats and guard it (or they try to guard everything at once).
The only time I would use anything at all aversive is to actually break up an on-going fight. Then that's only to break the fight up so more damage is not caused. The methods used to break up a fight do not help to solve the problem in the future (they are just to break up the fight in the moment). The trouble with having the dogs fight and having to break up a fight is the obvious that either dogs or owner could be hurt. But also, each time the dogs fight, their adrenaline levels increase and that feeling of "excitement" can actually self-reinforce the fighting behavior. Thus it is very important to try to not allow the dogs to "practice" the fighting behavior because the more fighting that they "practice" the more general tension there is, which can create a feeling of general animosity between the dogs. That may be why now they sometimes seem to fight over "nothing". I have noticed that sometimes the tension from a previous fight will lower the threshold for the next fight. Thus, you may notice that they may be more prone to fighting if they recently had a fight. The initial thing that you need to do to prevent further fighting is management of resources. Resource management is explained further on in this answer.
Here are some methods that can be used to break up a fight should one start: Breaking up a dog fight is a surefire way of getting bitten. Instead of putting yourself in danger should you need to break up a fight, you need to have a battle plan that will keep you safe. Things that can help you break up a dog fight are a hose, pots and pans (banging them and throwing them), a marine air-horn (blast it), something to slide between the dogs, something such as a blanket to toss over the dogs. In case your dogs should fight, you need to have the pots and pans or air horn or hose in a location where it is easy to access in a split second.
Because you cannot let your dogs "practice" the fighting behavior, the first thing you must do is to manage any of the resources that they fight over. That means any resources that they even posture over - meaning stiffen, freeze, hard stare, eating faster, growl, snarl, bark, lunge, snap, bite - need to be managed. Management means being proactive, NOT reactive. Being reactive is yelling NO or punishing after the fact. Being proactive is to make sure that the triggers are not in place to set up the behavior in the first place. To manage the situation, do not leave treats or toys around the house that your dogs may guard. If you want to give your dogs treats or let them play with toys you need to put one of the dogs away and treat or play with the other. Then switch dogs. You can manage the dogs by using gates, crates or putting one in another room. Also, they should not be fed together. Feed them in entirely separate areas so they cannot get to each other's food. If they should guard the empty food bowls from each other, pick up the bowls. If they should even guard their feeding areas, make these areas off limits except during feeding time. Some people choose to feed their dogs in crates to make it easier. Also stop giving your dogs high-value treats such as bones, rawhides, pig ears, etc. The best treats are really small ones that they can immediately eat and that do not leave any crumbs. If you feel you must give your dog something to chew on, it's best to do so in a crate or in a separate room. And make sure you remove the chew toy or bone prior to letting the dog out of the crate or room. When you give your dogs a biscuit or other treat, make sure they finish it completely and do not decide to hide or bury it in the rug or couch, since hidden treasure can start a fight.
Owners of resource-guarding dogs often report a "Jekyll-Hyde" quality to their dogs. They report that sometimes they get along fabulously. You mentioned that the dogs seem to only fight when you are around. That could be due to you having food and them getting guardy over the food that you are eating or the dog treat that you are holding. It may also be due to the dogs actually treating you "as a resource" to be guarded from each other. Or it could be due to you actually giving attention for the guarding behavior (the truth is that negative attention - i.e. yelling NO - is none-the-less attention). So your attention to their behavior may actually be helping to reinforce it.
If your dogs could be "owner guarding" - the type of behavior that people call "jealous" behavior. For example, when you pet Wiley and Nesey mouths/bites Wiley or your hand I would suggest first managing the situation and putting one dog away while you pet the other. Also, I would highly suggest getting both dogs basic obedience training so that you have some management tools under your belt. Obedience using positive reinforcement will open the channels of communication and strengthen the relationship between you and your dogs. It would be best to get a positive reinforcement trainer to actually come to your house so that they can personalize the lesson for you. You do not so much need an obedience class that will work on set exercises. But, you do need a trainer to help you teach and perfect a sit, a lie down, a send away to a mat or dog bed, a solid stay, and possibly even teach the dogs take, give and carry (i.e. a solid retrieve). The other thing that you need is to learn how to be a better leader to your dogs. Being a leader means being proactive and not yelling NO after the fact. It means having obedience commands (also known as cues) as a tool you can use - which means you have to be able to get your dogs to respond to your cues. The other thing that will help your leadership skills with your dogs is the NILIF program (nothing in life is free). The following web site explains the NILIF program in great detail! http://www.blackacorndogs.com/train_nilif.html. Training and leadership will also help you control the situation when Nesey is tired and does not want to play and Wiley starts to pick on her and play rough. This is a time where you would need to be able to give Wiley a command and reward him for going to his dog bed or mat. Also, this could be managed by giving Nesey a place to sleep so she is not being bothered. Thus, I would definitely crate train her (teach her to like going in the crate with positive motivation - a trainer can help you with this) and then when she gets tired and is lying around, get her to go into her crate to rest. My dogs actually choose to go into a crate to rest because it's out of the way and quiet.
Because dog to dog food guarding is so natural and hard to prevent, many trainers do not worry so much about it. The reason they don't is that oftentimes it happens without any actual damage (i.e. the dogs are just growling and posturing and no one ever gets hurt and it is not escalating). So, in a case such as that, it would be okay to not treat the resource guarding and just let the dogs work it out. However, in your case, the dogs are doing damage to each other - they are causing punctures and making each other bleed - thus, you need to do something other than "let them work it out". Also, their aggression seems that it might be escalating.
Do either of them guard resources from you or other humans? Can you take treats and food from them without them growling, stiffening or giving you a hard stare? If you cannot, you need to get the book "Mine!" by Jean Donaldson and follow her protocol for food guarding. To find this book, check out my web site at http://www.personalizeddogtraining.com/ and click on the Doggy Marketplace in the upper left corner. This takes you to links for several dog book sellers. If your dogs are guarding food from you, I'd highly suggest getting a qualified trainer to help you with this protocol. It's important to work gradually and do what you need to do to not get bitten. At any rate, I would suggest putting your dogs away so that they cannot beg when you are eating.
If your dogs are not aggressive when you handle their food, I would suggest to hand feed them sometimes - if it's kibble you can hand one piece at a time. With the raw food, "hand" feed using a spoon. When you do this, the dogs must be in separate rooms to eat. Also, it's always a good idea to teach your dogs that your hand provides even better food while they are eating. So, first when they finish eating, drop an even better treat into their dish. Work to the point that your dog knows that a human hand near the food bowl means even better food is coming. Eventually, work so that you can drop a really good treat in your dog's bowl while he/she is eating. Continue to feed your dogs in separate areas.
You cannot improve the dog-dog resource guarding the same way you can improve dog-human resource guarding. The reason for this is that with dog-human resource guarding you can work to teach the dog that "good things always come from human hands". With dog-dog resource guarding, the other dog really dogs want to "steal" the resource.
So the thing you need to begin with is to manage all the resources. They cannot be left around or given to the dogs when they are together. Of course accidents can still happen (i.e. one finds a chicken bone outside).
Next you can apply some dog-dog resource guarding modification techniques.
The first technique is to gradually teach each one dog to love having the other dog nearby in the formerly charged scenario. In many cases one of the dogs will be the "guarder" and the other will be the "non-guarder" (also called the "stimulus dog"). Since both of your dogs seem to be guarders you will have to teach the procedure with one of the dogs as the guarder and the other as the non-guarder and then switch roles. I'd probably start with Nesey being the guarder first and work the whole routine completely through with her before switching roles. For these techniques, it helps greatly to have two people involved and committed - you need one person to control the "guarding" dog and the other to control the "non-guarding" dog. Thus, I'd suggest hiring an in-home trainer to help (so your trainer could actually be the second person). The first technique teaches the "guarder" that when the "non-guarder" is present and gets a treat, that praise and a "jack-pot" of treats will soon be given to her (the "guarder"). You can start by tethering your two dogs at a distance apart in the same room and telling the "non-guarder" to sit and giving a treat, then walk over to the guarder and praise and give a jack-pot of really good treats. Take a break for a few minutes and repeat this. Also, vary the time that the break is so that the technique is not done in a predictable "rhythm". You want the "non-guarder's" treat to predict the treat being given to the "guarder". You don't want your timing or the fact that you said something or reached for the treat to predict the "guarder" getting treated. The next step is to have the "guarder" tethered in the room and to have a second person walk the non-guarder into the room - keeping him at a distance from the guarder. After the non-guarder enters, you will hand him a treat (don't reach for the treat until after the dog enters the room. Then praise the guarder and walk over and give her a hand-full of treats. The rest of this procedure is spelled out in the book Fight! by Jean Donaldson. To find this book, check out my web site at http://www.personalizeddogtraining.com/ and click on the Doggy Marketplace in the upper left corner. This takes you to links for several dog book sellers.
Another technique uses operant conditioning (i.e. awarding behaviors) to train the "guarder" to walk away from the "non-guarder" with the resource in her mouth. This involves first teaching the guarder a command to go into another room (i.e. leave the room). Then teaching the guarder to carry something that she usually guards with her when she leaves. This is all taught without the "non-guarder" present first. This method is also spelled out in the book Fight! by Jean Donaldson. This method might not work as well for your dogs since they both are prone to guarding.
The final technique also uses operant conditioning (i.e. awarding behaviors) to work on the problem. In this case the "non-guarder" is taught to go to a mat or dog bed in another room. The reward is a jack-pot of treats and the owner hanging out with the dog for at least 5-minutes. Then the "guarder" is tethered near a resource that is usually guarded and the non-guarder is sent into the other room to the mat or dog bed for his treats and petting award. This method is also found in the book Fight! by Jean Donaldson.
In conclusion, there are several dog-dog resource guarding modification techniques you can work on, however, management may go a long way towards improving the situation - plus, even if you do the techniques, you need to be using management so that no fighting is occurring to mess up the training/desensitization process. Furthermore, I would highly suggest hiring an in-home trainer, at least to help you with basic obedience and leadership.
I hope this is helpful.
ps this answer took a lot of work, please consider a bonus for this! Also, if you have any additional questions about my answer, I would be willing to clarify.
Good luck with your dogs.