Honestly, in your shoes, I would send her to public school. If she really doesn't like it there, maybe that will be incentive for her to obey you at home. And maybe she will thrive in the public school environment. If it turns out that public school is making her, and all of you, miserable, then you can always pull her out at Christmas, right? But it sounds like homeschooling her is not working out, and you have trained professionals advising you to try public school, so why not give it a shot?