That's good input, about Jill being an indoor/outdoor cat previously. Having brought in adult ferals who had never used a litter box before, though, my experience is that after a few days of peeing on the floor, and my dabbing the pee from there into the box, they used the box well. So her reason for not using the box shouldn't be simply that she prefers an outdoor litterbox. If you are dealing only with a behavior problem, she could be making a statement that she is angry about being cooped up and it may well have nothing to do with whether or not she likes using a litter box. She is, obviously, very upset, as are you and so you are both in a difficult situation. She's lost her guardian, her home, and her outdoor privileges, and she's living with people who wish she wasn't there. You are living with an angry cat that is making your home smell bad and creating a lot of extra work.

Can you fence off an area outside for her to use? Are the regulations simply that she is not free to roam? I know, more expense for you! A few people o this forum have created outside, enclosed runs for their cats so hopefully they can help. Perhaps you can start a thread asking for ideas?

What were your feelings towards Jill when she lived with your grandmother? Did you rather dislike her then? I'm wondering if you tried to bond with her, to spend time with her, to give her a new guardian. I know very well that it's difficult to spend quality time with a bad-tempered cat that is causing trouble instead of those whose company you enjoy, but creating a better emotional atmosphere between you might help.

There have been a few times when I've been totally and adamantly convinced that a cat with litter box problems is doing so for purely behavorial reasons, based on past experience with them, and then found out that they did have a UTI. It could be both, as it has been with some of mine.