What I've learnt with my two is that teenagers go through phases. Sometimes they are 'normal' and sometimes they are nightmares to the point of questioning everything we've done for them until then and making us worry that there is something very wrong with them.
I experienced with with my DS when he was 12. He was rude, showed real anger problems, argued over everything, any response I got from him was aggressive, slamming doors, and at the same time, appeared very withdrawn, not wanting to come out of his room, not showering, room looking like a pig sty and suddenly, I was convinced that he was suffering from depression.
By the time I had made full plans to deal with his being depressed, he seemed to suddenly totally snap out of it. He started to engage in some conversation, I was able to ask him to do something without him shouting back, and I even started to see the occasional smile! Since then, there have been ups and downs, but certainly getting better each month. Two years later, the anger outbursts are rare, and even though I still get some huffing and puffing, he is much more accepting of my requests, ok, orders!
Whatever you do, don't show that you are losing control. She will herself feel anxious about her behaviour and not understand why she feels so angry all the time. Your DH telling her that she is upsetting you is only going to make her see you weak and that's a dangerous position. She needs to be clear that whatever her behaviour, you remain the boss and the one that makes decisions and impose rules, not the other way around.
It's utterly exhausting to be constantly battling with them for the most simple things, those who we thought we had long established when they were younger, but do hang on and continue to stick with your demands and rules, otherwise, there is a risk that the roles become reversed before you know it and she starts ruling the roost.