Agree that MN cannot help as this family will need professional help. The dd is not engaging with that atm. @cheshirecat2913 I am wondering have you ever told her sharply and firmly that what she is doing is very wrong and she needs to stop it or are you always giving her a space to rant and complain about the girl in school? Have you mad it clear in a sharp and angry way that she is to stop this?
Along the lines of "I get that you're not a fan of Lucy, but you're wasting too much energy focusing on her. Your success is in your hands, not anyone else's. Not everyone can be popular, and that's perfectly fine. Most people aren't, and they still find their own happiness and their own group. We don’t act out of jealousy or try to bring others down. Stop comparing yourself, and start owning your own path. You need to take responsibility for your own actions."
or "If this behaviour doesn’t stop, I’ll have to take away your phone for a few days to help you reset and focus on what really matters. We don’t let jealousy take control, and you need to manage your emotions better. Our family doesn't stand for that sort of behaviour. Let’s turn this around, what went well today?"
or
"You have so many great things going for you right now, but obsessing over Lucy and being rude or aggressive will only hurt you. If this continues, it could lead to serious consequences, like getting expelled, and it definitely won’t make you popular or successful. If the behavior doesn’t stop, I’ll take away your phone for a few days. You need to focus on the positives and put your energy into building your own path. What went well today?"
Please don't pussyfoot around this issue with your dd because she has additional needs. If she isn't engaging with support services, you need to keep a very close eye on her and keep her busy with things that help her feel positive while making it damned clear that her attitude towards the girl is wrong and unacceptable.