Sorry for the delay. It took me a few minutes to attempt to consolidate your question and move the answers to this question and try and release the request on the third one you submitted.
They do make indoor fence products that are made to prevent dogs from entering a specific area which can allow you to make certain areas of your house off limits to your dogs. Here is a link to a site that sells this system.
You need to use a good enzymatic cleanser when cleaning carpets to remove odors completely. Steam cleaning is thought to actually set the smell into the carpet rather than remove it. In some cases, the padding (not a problem with oriental rugs) needs to be replaced and the carpet cleaned to stop the dog from remarking. You can read what one cleaning company has to say about the problem here:
Here is a site that also goes over the subject.
Vinegar does not work and in many cases attracts them to the area rather than away from it.
I'm going to give you three house training methods for training dogs to pads and I'm going to give you information on crate training as well. Perhaps one of these methods will allow your dogs to be house trained. Some smaller dogs do tend to take a long time to house train.
For training to pads or paper, this is the best way to go about it with the least amount of stress on your dog. It will take some effort on your part.
In the area that you want him to use the pad, set up an enclosure. You can use child gates, free standing pet enclosures, or anything that will serve to enclose the area you want him to use. These are the times when you will be taking your dog to the enclosure. When you feed or give your dog water, first thing in the morning, last thing at night and after extended play times.
You will want to start this when you are not working or when you can spend a couple of hours in the morning and evening exclusively doing this. Enclose or barricade the area and put pads over the entire area. Scent one of the pads and place it where you will leave it when there is only one pad. When you and your dog get up in the morning, instead of taking him outside, take him to the enclosed area and put him inside it. You can leave him a few toys but basically put him in the enclosed area. It is best if you can stay there and keep an eye on him. Do not engage him with talk or play or reassurances. Just be there so you can see him when he actually goes. He may be reluctant, but do not cave in to whines or cries. You must remain calm and in control and ignore him. Sit in a chair and read or do some other activity to keep you occupied while he is in there so you are not focused on him but can still see him. It may take some time, especially the first time, but he will eventually go on the pads as he has no where else to go. When you see him start to go, you can say in a low calm voice “good potty”. It needs to be in a low quiet voice so he isn’t startled into stopping. Give him lots of praise for succeeding and perhaps a little treat and you can then remove him from the enclosure and open it up so he has access if he want to use it. The first time may take an hour or more, but if you do it first thing in the morning, it is likely to take less time.
Repeat this according to the circumstances I mentioned earlier concerning when he should be going and a few extra times during the day to try and avoid accidents. After a few times going in the enclosed space and being praised for it and getting treats he should not be as reluctant to go in the enclosed area. Continue to praise and say the key wood “Potty”. When he reaches the point where he is going to the bathroom almost immediately in the enclosure on the pads, you will want to start taking up some of the pads so only a portion of the enclosed area has pads. Repeat as if the whole area was covered. Your dog should go on the pads and not the floor. If he does, continue the praise and treats. Slowly reduce the number of pads in the area until you are down to one or two only. If he should happen to miss the pad or go off the pad, add some more for the next time as you probably were taking them away too fast. At this point he knows the pads are where he should be going.
Once he is going on the pads and you are down to one or two pads, don’t close up the enclosure when you put him in it. He should still use the pad as he is now used to it. When he does, again praise, praise and more praise, let him come out the opening. Continue this process if it is necessary, but with the enclosure being open, you may now find that he is going there on his own. Once you notice he is using it without you putting him in there, you should be able to take away the enclosure or barrier. He should now be trained to use the pad.
Depending on how quick a learner he is, you may find he starts going in and using the pad early. If so the barrier can go earlier, but you should still only slowly reduce the number of pads he has to go on, so he doesn't miss, use the floor and think it is ok.
Second method is similar but you would leave him in the enclosed area all the time unless you are taking him for a walk, and just slowly removing paper and decreasing the area inside the enclosure that is papered. As long as he continues to use the paper, you are not moving too fast. Once you are down to a small area, he should be trained. I suggest this because while the dog is contained in an area with paper, the dog may not be as stressed as when there is a cage all around him.
Set up a contained small area with the paper. Then you will have the dog on a leash attached to you. I attach the leash to a belt loop on my pants. This way he is always where you can observe him easily and stop him before he starts urinating and place him in the potty area. When you see him start to lift his leg or squat, give a quick short tug on the leash and in a low toned, firm voice say "NO". Do not be upset. Pick him up and put him in the potty area. With this method it is best to just stand outside the area looking around ignoring the dog until he goes. Remember praise is everything.
A few key things to remember with dogs. You can not yell at a dog. It does not teach them anything even if you are yelling when they are doing the bad behavior. To a dog a high tone, loud noise is associated with play such as yips and barks from another dog. With a dog all commands and corrections should be in a low toned, firm voice. A mother dog corrects their puppies with growls and nips. Other dogs command them with growls. Also, no correction or punishment for accidents unless you can catch him in the act and then the correction should be as outlined above. If you use one of the non-leash methods, you will want to let him trail a leash so you can grab the leash and make a proper correction if it is needed when he isn't contained.
I also recommend a long walk each day with this dog to establish that you are the alpha dog and if you can possibly do it, an obedience class.
Below you will find the way I crate train dogs, which has worked consistently for 15 years. If you have other dogs you will need to separate them when taking them out to go to the bathroom, as they will want to play rather than potty.
I would also always take your dog outside on a leash. An unleased dog can run into the street and get hit by a car, or get into a fight with another dog and be seriously injured. Do this even if you have a fenced yard. No playing with your puppy during potty time either.
During crate training, you will be having your dog confined either in a crate or confined to a very small area which optimally will only allow the dog room to lay down in. Dogs will generally not soil an area where they sleep.
When you feed or give your dog water, take the dog immediately outside to go to the bathroom. Also take the dog out first thing in the morning, last thing at night and after extended play times and when they wake up after a nap. Take your dog to an area where you want your dog to go and preferably one that has been used previously. Allow your dog approximately 10-15 minutes to go to the bathroom. If your dog doesn't produce, take your dog inside and cage them again. If your dog does produce results allow her some uncrated time as a reward before crating or containing the dog again.
If your dog didn't go to the bathroom, take your dog out again about 30 minutes later and repeat this until your dog goes. Praise your dog profusely when your dog succeeds and is on the leash. This will teach your dog that it needs to go when you take your dog out and not play around first.
Some dogs learn quicker than others do, but once you have your dog going when it is on the leash and each time you take your dog out, you should be able to stop containing your dog. It is a lot of work, but pays off in the long run. Remember no playing or praise until your dog succeeds in going outside on a leash.
The key is no time outside of the crate unless you can have your eye on them constantly to pick them up and take them out if you see the classic sign of impending bowel movement or urination. Also, scolding a dog for going in the house does no good unless you catch them in the act. If you do catch them, a firm NO and trip outside should be done. Remember to clean any area inside they have gone with a good pet deodorizing cleaner. Here is a site with more information on crate training.
This is how I house train all my dogs.
In addition, put a bell or other noise maker on the door low enough for the dog to reach. Each time you take the dog out, ring the bell. The dog will associate ringing the bell with going out and one day ring the bell to signal to you that she needs to go out.
I know you said that your dogs do not go outside, so you could modify this method and take your dogs to the pads or paper that you do want him to use.
I hope this information is helpful to you.