I am so sorry that you and your DC are having to deal with this frustrating situation. It sounds like she has already described the principal challenges: she and the teacher don't understand ("like") each other, and (without judging the accuracy of her perceptions one way or the other) middle-school peer dynamics are resulting in her feeling socially ostracized. These are real concerns, with substantial weight for young adolescents in particular, and, while she is still responsible for her self-sabotaging choices, it is perfectly understandable that this setting might feel impossible to her.
I wouldn't necessarily frame this as stubbornness or not trying. Children don't always see all the possible paths out of a situation that adults might be able to identify (so failing out of the class might appear to be the only exit strategy to her), nor are they developmentally particularly good at delaying gratification (e.g., tolerating an extremely uncomfortable situation for the sake of access to appropriately-challenging math instruction).
I would suggest picking a low stress, low confrontation moment, and mutually discussing what would make her school experience better, and how you and she and the school can work together to make sure that her educational and social needs are met. When I have these kinds of conversations with my students, I always preface them by saying that I can't guarantee that we can get them everything they want (almost certainly, there will have to be compromises on all sides), but at least we can get a better understanding of what's interfering the most with their school success, which will help us to work as a team in putting them in a position to achieve their life goals (which can be short-, mid- or long-term).
In this case, it seems to me that the obvious first solution would be to get her moved to the class where the other 7th grade advanced peers are. But it would likely be with the understanding that a) you still take the consequences for your choices during first term, so some or all of those grades may have to carry over into the new class, where you will have to work extra hard to make up for them; b) once we've addressed this, we're all going to move on--no ongoing complaining about the old teacher, and definitely no badmouthing her to your new classmates. (It is highly likely that a) will be a condition the school requires, and my preference that b) be required, both so she doesn't get herself into trouble with staff, who have their own relationships with each other, and may have already talked about her, and so she doesn't trap herself emotionally by brooding over past wrongs incurred, in her mind, by the teacher or peers.)
And if something doesn't seem right to you, who know your child very, very well, then it's definitely worth following up on. I'd be careful, though, about going in with any kind of assumptions about who is "at fault", if anyone.
