Sorry to hear you're having a tough time, M.
I think it's too much pressure for you to have to take. It's a lot to take on to study full-time and look after two almost-grown girls, especially if one is being really difficult. She's obviously acting up for some reason, but it's unfair to you and your other sister that she's being like that.
I think you should try talking to her, and explaining that you want the three of you to be a family and you need to support each other, and that her being the way she is, is not being supportive. Tell her, you know that life seems hard sometimes, but it's tough for everyone, and she needs to pull her weight aswell, because you need support sometimes too.
If that doesn't work, you'll have to make a tough decision, and tell her that if she carries on you have no other choice but to let one of your aunts take her. It's not fair on you and your other sister, and who knows, maybe your middle sister will benefit from a different environment with your aunt.
All the best.