What breed of dogs are they?
Are they male or female? Are they fixed?
I would suspect the one who will not go out the doggie door.Something may have frightened him so that he finds it safer to stay inside. What you can do is buy crates and crate them when you are not home and this will give you a clue as both are old enough to hold it for at least five hours.
Two male dogs will also mark territory so if there has been any change in the home, new animal, baby, company etc. then that can cause a marking war. Normally they don't like to mark where they eat and sleep so something is going on between them.
I would only allow them to eat when you are with them and pick any remainder up right away as soon as they walk away from the dish.
I would also wonder if there isn't a health problem such as a urinary tract infection as this will have a dog go in inappropriate places. A simple urine test will show this.
I would definitely work on the one who is afraid to use the door and I would not let either have full run of the home without you being there to watch them . For now, gate off a room that is easily cleanable. You may want to gate off two separate rooms so you can see who is doing this.
For urine odor use a mixture of white vinegar and water. IF it is an area where bleach won't harm anything such a tile, use that in the mix as well.
Well, if it is due to marking, which is suspected, the only thing you can do is not to allow them to have run of the home. Dogs marking is an instinct and any type of punishment does not work with that. I have one that marks so he is kept on a six foot tether when he can not be watched. This has solved the problem. You may also want to sprinkle down some kibble or treats in the areas that have been marked so they learn it is an eating place not a peeing place. Belly bands also help. Retraining them that you are the leader of the pack can also help so there is no competition.
I'll direct you sites on marking which may help you further.