Your sister is lucky to have you in her life though, you sound like your priorities are on point for one so young. If I were in your situation I would just think of my mother as a source of free rent (if that is the case) and concentrate on your school, as long as you and your sister are in a safe environment; if you have enough to eat and are not exposed to any immediate danger. Possibly your sister would qualify for disability, you could file for caretaker status, and eventually you two could get a place together, though you may have to be on your own before applying for assistance.
Perhaps your mother feels that if she's putting a roof over your head that's enough, even though anyone with half a grain of sense knows it's not.

I feel rejected by my mom too; it hurts at first, but I haven't seen mine in years. I miss her, but not much.