You're not wrong to be fed up with this, especially if your sister-in-law is taking advantage like it sounds like. You need to really have a serious conversation with your wife and let her know how you feel. I can understand that she feels like she needs to take care of her sister if she's going through hard times, but you are only enabling the sister in law if you're not holding her accountable for some of her actions and making her responsible too. She can go to school and still work part time to make a contribution to the household. If your wife can't see this for herself--and especially if you can't sit down and have a serious conversation about it with her, without her getting offensive and starting a big fight, then I would say you have every right to give her an ultimatum. Let her know that you are serious and that you want to help her sister, but you're not going to be taken advantage of. Tell her that there need to be ground rules and that she needs to not step over her boundaries and contribute to the household as well.
I hope it works out--Good Luck!