So, a couple of thoughts:
1. I expect a significant amount of this stress is from early puberty hormones. Those things start around 9-10 and get worse over time. This does not affect just her, mind you -- it causes repeated shifting of friend relationships and groups, which is particularly difficult for kids to manage given their own hormone overloads.
2. Does your kid have any behavioral/learning issues otherwise? My DD was both very smart and very ADHD, and so we had ridiculous homework battles and meltdowns simply because she was so exhausted at the end of the day from trying so hard to sit still and behave that she couldn't handle any more. These kids are very, very difficult for schools to manage, because there is a tendency for schools to think that "academically advanced" = "psychologically/emotionally mature" as well. Which is often not the case. So even where your kid is more than bright enough to handle the workload, she may not be emotionally mature enough to tackle it at this point.
3. How are the "advanced" classes treating her in general? Not in terms of grades, but in terms of grasp of the subject matter, appropriateness of the homework (level/quantity), etc.? Some schools treat the "advanced" classes as simply doing the same thing a lot faster. Sometimes that means it moves too fast for a kid to grasp everything (mine is whip smart but needs time for concepts to settle in, for ex.), and so you get anxiety from the constant rush/pressure. Other times it means that they just pile on the "normal" homework in half the time, but the homework itself is largely busywork and not really helpful or necessary. And beyond that: do your DD's teachers like her? Do they think she is a fundamentally neat person with a lot of promise? Or do they just sort of internally roll their eyes at her complaints about homework or grades or whatever? Kids can tell the difference between teachers who like them and teachers who don't -- and if you have a sensitive, highly-strong kid, that will absolutely come out in her behavior. (Ask me how I know)
4. On the other side: if you do online school, you will be in charge of it. I'm sorry, but I don't know any wound-up preteen girl who is going to happily go do her lessons at the appointed times, whether there's a teacher there waiting or not. Her being home all day will just give her that many more opportunities to whine and complain to you about the unfairness of it all and how much she hates school and all that. Added bonus: with no friends around to interact with over the day, you also get to be her social outlet. Fun!
5. I know it's trite, but is there anything going on at home? I swear, my DD was the canary in the coal mine -- she could tell I was stressed before I even recognized it myself.
6. All that said: start with some therapy. There is clearly something not right here -- it could range anywhere from pure hormones to a very significantly bad school situation that she is not telling you about to her knowing how to push your buttons. And it's probably somewhere in-between all of this. Before you make any decisions, I would suggest taking the next few months, and even over the summer, to talk to a therapist to try to get to the heart of the problems here on all sides. And you also need to consider the alternative school option not as a panacea, but with a very realistic view of exactly how much additional stress that is going to put on you to manage -- when my DD was that age, I'd have happily paid someone to get her out of my house for the day. ;-)