From what you've described, there's no doubt your niece needs support. No amount of love you have for her is going to provide it if she is coming from a home situation where she's alienated and dismissed. Who knows how much of those dynamics are contributing to her acting out, and not her disability. (I'm just going to ignore the sociopath dx. How can that even be diagnosed at that age--I mean...teenager.)

Anyway, I just say all of that because you care about her for a reason. She's a kid who's gotten a raw deal, and you have empathy.

The thing is, there is absolutely no way to help her by colluding with the family dynamics. One way to put a halt to it is to contact authorities regarding her claims of abuse. And let her know in no uncertain terms that an eating disorder requires professional help and you won't be part of watching her enter into that without speaking up or doing something about it.

In other words, you redefine what love looks like and be the adult that she needs. That can't happen by sacrificing your well being for the sake of family dysfunction.

She could get mad. The family will get mad. But is that any worse than a lifetime of this, which is where this is headed?

eta: oh...and do not have her over to stay with you for Easter.