There are a few things you can do, it isn't hopeless! I have more cats then kids and a few kittens so I am no stranger to accidents. What you did is GREAT but another solution is equal parts vinegar and water in a spray bottle, and spray the area down (after you clean it) cats don't like the smell..ok neither do we but it goes away pretty fast for us. You will also need to keep the room closed to them for a few days. Once you open the room back up to them be prepared to watch them and make sure that they are not sneaking back over to that area, if they are then squirt them with a spray bottle...they do get the hint if you are persistant. Baking soda sprinkled on the area over night (sometimes twice) will also get rid of the smell.
I am glad you asked instead of just jumping to the conclusion that the cat has to go. As to the fighting, cats go through phases were they love each other then hate each other, but the older they get the more solitary they become and the peeing is probably a way for them to show who is the dominant cat. I am not sure how to fix that...mine will just fight and when they do they get put outside.