The teachers need to step off and stop sticking her with them. From the given bullying and “I’m the only one who will accept you” type behavior, she sounds manipulative and her behavior will only get worse if the teachers force them together and she can isolate your sister. If this is the only reason they hang out, I would be telling the teachers to keep her away.

You need to go to the administration or call them and tell them that this is unacceptable behavior on her part, and on the teachers part to try and force them together. Also keep in mind that they might want to gloss over it and not create a problem and “kids will just be kids.” They should not be going out of their way to create an unsafe environment for her. If necessary, you may be able to file a formal complaint to then school district. If it comes down to it you might be able to sue the family for emotional distress, but id recommend starting with the the teachers first. Call the school and ask to speak with them I guess