I agree, Boffin, that the DD is very angry. Teenagers often are. There are real reasons for them to be, and not-so-real. Most of them are pretty powerless in their own lives and that makes some of them furious. A lot of them are also angry with themselves, IMO, because they can see themselves behaving or handling situations badly.
And for almost all teenagers, mum is the person closest to them; the easiest and safest person to dump all their anger on. It's understandable, but it is never justifiable. Everyone - especially every adult - needs to learn to manage their own anger so they control it and do not use it to hurt people, even or especially the people closest to them.
I have learned (to my cost, over several years) that if you are a mother of a teenager who behaves violently towards you, it does not help to try to understand the reasons. Trying to understand the reasons keeps you locked into a situation where you believe, and your child believes, that you are responsible for their behaviour: that if only you could work out why they were behaving like this, you could stop them. 
But you can't: only they can stop themselves. Whatever the reasons, as bubby said, it is not OK to be violent.
Most of us do already (kind of) know this. But when you're caught up in it, it is so easy to forget. Because you do feel that somehow it must be your 'fault' if your child behaves like this. Our whole culture tells us children's bad behaviour is mothers' fault. Personally, I thank goodness that I have another child who is (by comparison to DS1) delightful, or I would definitely have thought I was a shit mum.
In the OP's case, last night the 'reason' was the car. No doubt if the OP had lent the car (or filled it with petrol, or paid the insurance, or polished it nicely, or whatever ), DD will claim she would not have 'had' to lose her temper. But that is bllcks. Of course it is. Other people deal with not getting what they want without becoming a violent thug. DD will probably say, and maybe believe, that if only the OP hadn't made her angry, she wouldn't have been violent. But the problem is not getting angry - everyone gets angry - the problem is that she is losing control of her anger and using it as an excuse to be violent.
WTF, my DS was angry with me for calling the police, and incredulous. That was at least partly because I had not 'drawn a line' before. I dealt with months and months of bad and violent behaviour, trying to work out 'why' and what I could do about it, before the penny dropped for me. When he said "How could you?!", what I said to him was "I can't stop you. You have to stop yourself. And if you don't, then I have to call for reinforcements like the police." Maybe these words will help you too.
If I were you, I think I would call the police this morning and have your daughter arrested. She has assaulted you, and if you have a black eye, there is enough evidence for the police to charge her with assault and actual bodily harm. I am not you of course, and only you can decide what you will do in this situation. I'm not pretending it will be easy - it will be difficult. :( But the alternatives to not making a report today are bad: either you wait for the next attack, and then call 999; or you wait for the next attack, and you don't call the police, and it happens again, and maybe again and again.
You can't control their behaviour, but you can control yours. Take some action to keep yourself safe. You deserve to be safe, and happy.