P.M.
There are lots of possible approaches to this problem.
For starters, it sounds as though your daughter is either more emotionally sensitive than most, or could be reacting to foods, food additives, or other factors in her environment. I am severely sensitive to airborne chemicals like perfume and auto exhaust, and some food colors and preservatives,. Exposures can leave my nerves raw and my temper short, among other symptoms. Allergies and sensitivities are common in kids, particularly if they get lots of commercially prepared foods. And for a child, coping with a mood swing would be much harder than for a grownup.
Next, I used the following approach for a few years, working with at-risk kids as a tutor in a high school, and had remarkably good results with many of the kids (even some who had been in repeated trouble with the law). I would simply observe without judgement what had happened, and ask the kid what their version of the story was. They might have a really exaggerated view of how abused they had been, but I would simply acknowledge that "that must have felt pretty (awful, unfair, frustrating)."
They would frequently be surprised at my sympathy, and relax, maybe even say some more about the event. I would continue to affirm their feelings. Eventually, I would ask how they thought it would feel to be the other person, maybe to consider why they had said or done what they did, or why they were required to do it (as in a teacher keeping order in a classroom, for example). I would sometimes coach the kid a bit to help them see the other side, but always avoided pressuring them for the "right" answer.
If we got that far, and we often did, I would ask what the kid might have done if he was the other person. I was amazed at how often a moment of surprise would cross the kid's face when they realized that they might have acted the same way as the person who had made them mad.
There is an internalization of understanding and the beginnings of responsibility for personal choice that would sometimes be born in that moment. It's a beautiful thing to see. At that point, you might even be able to ask what consequences might be appropriate, and the kid might assign himself a punishment or require an apology for his own behavior.
That's not the end of any story, of course. The first dawning is only a start, and the hard work of learning to respond consistently follows. So if you try this approach, be prepared to move slowly, be as gentle and supportive as possible, and repeat, repeat, repeat as necessary. And remember that your daughter will exhibit the high impulsivity that is part of being a kid, and will gain self-control only gradually.
But with that self-control will come self-respect and a desire to win the resepct of others. (Respect is one of the most rewarding feeling a young person can experience – they get precious little of it from the "adult" world.)
So offering her empathy and respect might give her and you a surprising new approach to how she relates to you and to the world. And how she internalized the value of self-control. It might be worth exploring.
