You gave me a lot of information to work with. The problem you are going to have moving in together is that there can only be one top male dog in the house. If one is not neutered, that dog should be the top dog. If both are intact or both neutered, then the most dominant dog will be the boss or leader. Both you and your boyfriend will need to acknowledge that top dog first. It can be hard because you love your dog and he loves his and both of you are used to showing your dog affection first. It is natural. However, when the households are combined, the top dog should get attention first, fed first, let outside first. They get the treats first and you can't let the other dog push past the leader. The top dog has the right to get all those things first. If the humans acknowledge that then the other dog accepts it and there are less marking incidents and less dominance issues.
So once you figure out which dog is dominant, you have to treat that dog like I describe. That will help things go a bit smoother. The boss will have ownership of toys as well and that can be an issue. Usually over time, the submissive dog will be allowed to have toys but must give them up when the dominant dog walks over. It is simpler to just have multiple toys and give the top dog theirs first. It still might not work out but over time it usually does.
I would suggest formal training sessions for both dogs. It doesn't have to be classes but does need to be formal. Perhaps you could both do the training together and even switch which dog you handle every once in a while so the dogs learn to obey both of you. The following site is helpful in helping owners train their dog. Be sure and click on the link to the page on obedience at the bottom. and links on subsequent pages leading to detailed instructions.
Training works best if you train at least 30 minutes a day (two 15 minute sessions). I would start making your dog work via the Nothing in life is free program (NILF). It is outlined below.
Learn dog body language. It can help you determine who is feeling what and stop the behavior before it starts when it comes to aggression.
You can also reprimand with a low toned NO any aggression and reward any desired behavior toward one another. I suggest hot dog slivers for rewards. Most dogs will be happy to get those treats for behaving.
Now for the elimination issues. You need to be sure you clean properly. You sop up excess fluid first, then apply enzymatic cleaner letting it soak down into carpet and padding for at least as long as the urine did before sopping up the fluid once more then drying with clean towel as much as you can. When you move, I would get a special light that will show up old urine stains and be sure there are no such areas in your new house. If you find any, clean thoroughly.
The other thing you can do is feed and water the dogs on a schedule say twice a day as long as neither dog has a kidney issue. Then log when each one urinates or defecates. This gives you a general idea of when they need to eliminate so you can be sure they have access to the outside at those times. If there are times you won't be home, you can move the feeding or watering times to make it more convenient to your schedule as well.
I'd also try for at least two walks preferably a short time after eating such as in the morning before work (this typically is a shorter walk) and then a longer one in the evening before bedtime. Dogs like to mark their territory. Long walks around the neighborhood helps a dog establish that whole area as his territory and he will start marking all over on his walks thus leaving little to none left for marking in the house. Also if the house is within that territory, there won't be as much of a need to mark especially once one dog is the established boss.
Now what you might do is crate one dog to see if the marking still occurs which can help you determine who did the marking . A dog alone in a house might never have marked but once a strange dog is added might start just to let the other dog know they own the house.
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer so I am compensated for my time.