When he was the only dog around, there was no need for him to show territorial behavior. Now, his instincts are kicking in and as a result he is marking territory. Even though he's been neutered, it doesn't mean he has been stripped of his Alpha/territorial behavior. All dogs show this type behavior, either Alpha or submissive. His behaqvior is most likely because of the other dog coming into the picture. There will probably have to be some separation of the two dogs, even to the point where they can't smell where the other has been. Ht older dog is marking for dominance, not for sex. If the problem can't be solved, it may be that you have to decide between the two dogs.
And, it's possible he could have, or still has a kidney/bladder infection. Was blood work done when the diagnosis was made or was it made solely on the description of the symptoms.
These are the two possibilities I see. Hope you're able to find the solution without losing either of your dogs.