Well done Notcoolmum that sounds like a labour of love 
but very much worth doing! Hope your dd is appreciative!
That's the thing Billy normally I would have lost my temper and it would have escalated. Thanks to what I have learned from everyone on this thread, I think two things have happened (1) I had the parent-child dynamic at the back of my mind and I know now to disengage and walk away if that doesn't succeed rather than descend to child-child and (2) having learned I am not alone, I feel a a teeny bit bit less of a failure than I did, which has given me an inkling of confidence again, which I think has translated in to dd knowing "I mean it" ifyswim. And with more confidence, I'm not letting the criticism and insults get to me so much. And in turn, my reactions are less strong.
I'm certain that there will be days ahead when I will have just as much doubt again and feel very wobbly, but for now, I feel as though I have more clarity about what to do and how to stand my ground a bit better and DD seems better for that too.
I think the confidence thing is important because teens like toddlers (and dare I say it without sounding too awful ) horses and dogs can "smell" ones state of mind and push boundaries accordingly. I'm not saying it's a power play but that they can sense whether your intentions are "true".
For example, if you are telling a toddler "no" - when they are covering their own face with paint or something - but you are secretly finding it funny and laughing to yourself, they can sense you don't mean it. (I am not comparing children to animals but this very same dynamic comes in to play when training horses and dogs. They can read you so accurately that if they can "smell" fear or uncertainty of intention, they won't bother to comply. It's only when you are relaxed and have the confidence of your convictions that they do what they are told ifyswim. However authoritative you appear on the outside, it's how you are feeling on the inside that counts. )
Just to be clear; obviously parenting teens in not all about imposing our authority and making them comply. More about guiding them to make better choices themselves. But sometimes we do meet a brick wall and really challenging resistance which can be confronting in the extreme. And confidence is helpful in those situations. And knowing you can handle those situations, helps you with the smaller more insignificant ones.
And I think teens do in general benefit from having a fairly stable frame to rattle 
Apologies for yet more amateur pysch ramblings! Just feel relieved that the negative cycle seems to have stopped spiralling down for a bit here!
[Give it 'til 4.30 pm and no doubt I will be back on the thread moaning about something or other again ]
Thanks to all Po Ts for making it better for now 