I am going to be a bit controversial here, which is not really like me! Looking back to when I had my first two children, who are now 12.5 and 10, there was not all this emphasis on behavioural techniques, star charts, naughty steps etc. In fact, I seem to remember naughty steps were frowned on! Instead I followed the advice in my two parenting books, which was just really to stop the child every time they did something wrong, lift them away if necessary, tell them why they couldn't do whatever and just be persistent. Also, the best bit of advice ever from Rose Eliot, hardly a parenting guru, which was that the most important thing, above all else, was your relationship with your child. I didn't do star charts, ticks or anything else, and it seemed to work - not without hiccups and bouts of bad behaviour, but now they're both really well behaved most of the time, and great at school.
As I have mentioned, my ds2 was far more difficult, and the way I managed the others just didn't seem to work with him at all. Looking back, I think I just really didn't connect with him on some level - he is very active, and not at all interested in the sort of activities I would do with the others. In other words, my relationship with him was really bad.He would throw things, hit , scream, refuse to do what he was told - and all the while people would be insinuating I wasn't firm enough, but I was! probably too firm, and too strict, and always really assumed he would misbehave and pounced on any behaviour even if I would have ignored it with the other two.
So - very long winded, but I think if your dd is good at school, she can be good. If she is not good at home then there is a problem with your relationship with her, or a problem with something else at home,like not enough time to herself, or whatever. This is common sense.I do not mean this in a nasty way, as I have exactly the same problem. My ds has had a great experience at school - it is very structured, which he needs, no-one assumes he will misbehave, everyone thinks he is wonderful as he is old for his year, and very bright, and is very charming and popular. I try my best now to respond to him positively,and to think of our relationship first, even just by giving him a big hug when he comes into bed at 6am, and saying something like "lovely to see you" instead of "Oh God, it's too early, go back to bed," rant rant rant, which is what I used to be like. Have a think about her personality, and how something at home, or in your relationship may be frustrating it and causing these outbursts and see if you can change it a bit.
I hope this makes sense. It is something I feel quite strongly about, and believe me I have been in despair over my son's behaviour and really upset that everyone thought I just wasn't strict enough. There is so much emphasis on behavioural techniques now, that I think everyone thinks they are the be all and end all.This works better, for us. I really hope I haven't offended you, as I do know what it's like and know you will work it out, whatever method you choose, as you obviouly care for your daughter so much.