Sorry I didn’t see this until today, but I hope I can help.
First, yes, he is marking his new territory, and you are right about their resistance to change. My first suggestion is to remove all newspaper and bedding from his cage, as this is never a good idea when getting them to use a litter box. It is confusing, even if he’s used to it from before. I would remove it, clean his cage, and bear with him a bit longer when he pees in the cage without the bedding.
I would also suggest a bigger, new litter pan. It may not seem right to change his stuff now, but he might use it more, especially if it has fresh litter that he likes. Be sure you’re using what he is used to and likes for litter. Put it in the left corner, and if he still goes in the right corner, you can try putting the other one in that corner for a little while. (I know it will cramp him, but it’s one option.) That way he will probably get the message that the place to go is only in the litter pan(s). When you mop up pee in his cage, use a paper towel and put it, or a piece of it, into his litter pans. That puts his scent in there and is also a message to go there.
Did the new house have a pet in it? Because sometimes he can smell a former animal and is very busy marking, as well as afraid there may be one in the house. I would clean your house where he’s peed with a 50/50% mix of white vinegar and water, from a spray bottle. It will eliminate any other animal odor and also clean his own pee odor. It is mildly distasteful to bunnies, so will keep him from peeing in those spots again. (Hopefully). Clean his cage with it, then rinse well with water, in case he got something there that is upsetting him and he can’t mask with his pee.
I would only let him out for supervised free time while you’re with him and put him back or into his outer litter pan the second you see his tail go up. This should help him learn that he needs to pee only in litter pans. You’re basically starting over, but he is stressed and he needs to know what is his. He can stay in his cage longer until he gets settled into good habits again. I would do this for the next week at least.
FInally, be mindful that this may be due to an illness even though he’s seen a vet. I am glad you already had him examined so that makes it unlikely. I also agree that he is missing your mother. It’s harder for some bunnies to adapt to change than others, but all need to keep their stuff, their routines, their food and time of eating the same for a smooth transition. He can explore the new house once it is free of strange odors, but remember that it’s more scary to him than fun at first, and let him explore one room at a time slowly. He can also hear strange noises outside that you can’t, so he may be frightened by dogs barking or trucks or birds on occasion that you don’t notice. It all leads to bad litter habits.
Keep us posted on how it goes.