So what are your choices at this point? Maybe you should write them all down, weigh the pros and cons and try to make a decision that is the best for everyone.
You sound too stressed to go on this way. Something has to change. You seem to be doing penance for your past mistakes by caring for these cats for your family (parents?). But this situation is too much for you, and was for your sister, too, you said. Maybe it is too much for anyone, at least someone living in a studio apartment.
Maybe contact cat rescue organizations in your area? I really don't know, I'm grasping here for ideas. You've had a lot of suggestions here, and either they haven't worked for you, or you haven't felt able to try them.
The relative who offered to take Chan is across the country, right? And Chan's heart won't take the plane trip, right? And you aren't able to drive him, right? And your family, where ever they are, can't take either of the cats back, right? And you can't find a way to make the situation with the feeding and eliminating workable for you, right? Sounds like a situation that needs a rescue. I'm not saying take Chan to a shelter, at this point. Maybe there is an alternative. I hope someone here has more ideas for you.
I don't know if you said, but these cats have been neutered, haven't they? It Chan has not been neutered, that may be the cause of most of his problems.
If your sister couldn't handle these cats, and you have done your best for however long it has been, and it is making your life miserable, and you've done what your family suggested, and it didn't work, what do they expect you to do? If they are their cats, and you can't cope, then they need to come up with an alternative. It may not be convenient, or to everyone's liking.
Many people, at this point, would decide that euthanizing one or both of the cats is the only way. If you come to that point, please consider taking them (or one of them if one is tolerable) to a good (check it out) no-kill shelter. I volunteer at one and we keep cats for as many years as it takes to find them homes. Often they are surrendered by owners who just couldn't cope with them, for whatever reasons. If the cat is healthy and still enjoying life, they deserve a chance to find a more suitable home. And as I wrote in another thread, most of the cats living in my shelter seem quite content. Some people there foster cats long term in their homes, especially older cats. It is not the best solution, but it may be the only one left.
Please try to consider what is best for them, not what is convenient or comfortable for the people involved. It isn't just your problem. But if the others won't help and be reasonable about this difficult situation that you are dealing with, you have to do what you have to do - what you can live with. I don't think it is reasonable that you should feel that you have failed your family somehow because this isn't working out. It does sound like a really difficult situation that most people would struggle with.
Good luck to you!
Was he out enough for you to tell if it was helping? That'd help you decide how important it is to get him to the other family member so he can roam.
