Rodney

Stick it out for another year, take care of yourself. You can offer help to your sister, but if she doesn't want to take it there's nothing you can do. If she ever asks for help in a way that shows she really wants to work towards doing better, be ready to offer help and also be sure that, in the meantime, she knows that you will do that when she's ready.

But in the meantime... your mom is basically unwilling to do her job, cancer or no, and is selfishly trying to put it off on you; your dad is staying away from home and ignoring the situation; and both want you to fix it because they can't be bothered to, and don't want to take the blame themselves.

Do your year, thank them for their financial support in raising you, then leave, and say you'll be happy to hear from them any time they have a sincere interest in finding out how you're doing. If the situation gets worse or you just can't stand it anymore, spend as little time at home as possible; study in the library, whatever. Just go home to sleep, eat, and do your laundry.