I think she's going to be fine. That is very, very different to what you described in your original post.

She won't have what I, or likely you, would consider a good life. But she knows how to play people against each other and put on a good face. That can get a person way farther than most people like to face. She likely won't end up homeless.

If you or your mom are able to get her to treatment, one/both of you should try. Or the extended family can band together to help her. There is still hope she can have healthy relationships. I personally believe that healthy, happy people don't hurt others- so your sister manipulating and mistreating people is a sign of internal suffering that should be addressed.

But if worse comes to worse and your mom kicks her out, then I think she'll be able to survive and make things work. Probably not in a way you think appropriate or acceptable or healthy, but she probably won't die on the streets.

Manipulative people can get very, very far in this world.

I still do not give your mom a pass, for the record. In my opinion your mom has an obligation to do everything she can to fix her mistakes and try to get your sister treatment and help. She should've been harassing doctors since your sister could walk, and the second she found a therapist dedicated herself to getting your sister treatment. I have a special needs kid and know a lot of special needs parents- yeah, it's hard and sometimes scary and sucks. Suck it up, buttercup, that's what you signed up for when you chose to become a parent.

When she gets bored, she picks on my young niece and nephew in order to start a fight with my other sister

Ask your sister why she enables her children's mistreatment. Your sister needs to cut her off from her children, at minimum.