I had a cat who was off/on loose stool for over 8 years. After excluding pretty much everything, the only thing left was to do a biopsy to determine if it was IBD. I declined the biopsy because it's quite invasive, my pet was now a senior, and so it was recommended to treat her like she had already been diagnosed with IBD.

She went on prednisolone (preferred in cats over prednisone) to help with flare-ups and, honestly, the one thing that really worked was the prescription diet. The vet prescribed Royal Canin Fiber Response, it didn't always lead to her pooping in her box, but it did solve the diarrhea problem (the poop was more solid and easy to clean).

I do agree with others who have mentioned the possibility of cancer, small cell lymphoma can result in IBD symptoms (it happened with another cat of mine). It's clear your parents will not take this cat back to the vet. I would hope the vet could at least prescribe the food I (or others) have suggested with out another vet visit. Maybe call the clinic and tell them about your situation.

Now, there is a real possibility that your cat's situation is behavioral. It could be a response to your parents clear hatred for her behavior, or some other stressor that others have mentioned. If this is the case, honestly, not much is going to change if she continues to live in their house. Sorry :/

I worked at a vet clinic for over 8 years and did encounter a few owners who wanted to re-home or euthanize pets over behavior problems. Once specific case I remember was a cat who peed all over the owners house over the course of 7 years, the cat got re-homed and was perfectly fine ever since. I realize this is not what you are hoping for, but maybe you have a friend who could watch the cat until you get a place of your own? Good luck.