I don't think anyone can tell you what exactly is going on, just make suggestions. I have 6 children and 2 of them (boys) were like what you described. My oldest son had these behaviors for years and I researched and tried everything and learned a lot in the process. When he hit 13 he mellowed out so much. It was as if he just couldn't process how to handle things in a proper way and was very impulsive. He couldn't handle any form of rejection, mistakes or the word no. He went right into a fit. I still don't know what it was that mellowed him (hormones, better reasoning skills, or what), but feel a lot was tied to allergies. I've noticed that his allergies have been better since he's been better. My youngest son (6) gets like this if he's hungry, tired, or in any kind of pain (even just feeling lousy from a virus). I'm so grateful that I can pinpoint the cause with him. Every child is different and their coping skills vary.
Please don't feel like you're doing something wrong. Even the doctors we saw for my older son didn't have any answers set in stone. It was more or less, try this and see how it works. Kids at your daughter's age don't use reasoning skills as much as they are reactive.
Try logging her sleep hours as well as what she's eating. Keep track of when she has her fits, what condition triggered it (having to leave, hearing no, etc.) and how long the fit lasts. I learned that my oldest son had a lot of anxiety with change. He was much worse anytime we tried to do something different (even going to a park if it wasn't completely scheduled on a regular basis). You can't avoid change ever just so the child will be fine, so there is a learning curve on how to best handle it. If you can figure out what your daughter struggles with, you'll at least know more on what to try.
Some people swear by the Feingold diet so you might want to read into that. Kids nowadays have so many allergies and sensitivities to foods that it is really worth a try.