I should say I started this earlier this morning but got side-tracked, so apologies if everything has been covered already.
I am sorry you are going through this at the moment. I have had some run-ins with my DD of a similar age recently which have ended in slanging matches, which has been surprising and upsetting for both of us, so I sympathise.
It seems to me that there are two strands running through your post; how to manage potentially explosive confrontations with your DD, and also a need to explore your own past and triggers excuce my while I play armchair psychologist .
I realised quickly that I would not be able to 'out-shout' DD without actually frightening her, which could cause lasting damage to our relationship. So I had to think of strategies to nip confrontations in the bud before they escalate. Here's what helped:
-remembering that preserving her dignity and integrity in a disagreement is really important, so not frightening (shouting), intimidating (respecting physical boundaries, not towering over her or talking too close to her face), threatening (removing privileges or belongings), blaming or shaming her. Pretty textbook, but just that week I had already managed to escalate two big ding-dongs by metaphorically painting her into a corner by insisting she look me in the eye, raising my voice and blaming her for something, and threatening to cancel something she was looking forward to as a consequence. DD being DD, there was really only one way for that to go.
-working on the assumption that she doesn't want conflict anymore than I do, but is less experienced at navigate her way around tricky situations. As the adult it is my responsibility to be the bigger person and help her with the big feelings which arise when conflict is brewing.
-remembering that all behaviour is communication, and trying to see that what might look like 'bad' behaviour is her showing you her need for... well, that's where your conversation begins. In my DD's case it is pretty much always about wanting quality time with me without her younger sibling. Paradoxically, this unexpressed need tends to manifest itself as behaviours which, if I didn't know better, would make me want to lock myself in another room!
-distraction techniques! For some reason I find these really hard, and it requires me to be the most grown-up I can be, but so worth it. So easing off a little, making light of things and saying something like "Well, look at us, getting all het up about x. You know, I would much rather ring granny and tell her about the special merit for reading you got / pop a pan of popcorn / whatever. Let's sort this out later." It gives you both a breather and an opportunity to regroup and remember how nice it is like to get on. Then gently revisit later.
-being a step ahead, trying to meet her unexpressed need for quality 1:1 (in my DD's case, might be different for your DD) before it manifests as a challenging, essentially attention seeking, behaviour.
I really recommend Non-Violent Communication by Dr Marshall Rosenberg as a easy, yet illuminating, read. Even though it is not specifically for parents, it gives insight into communication in all relationships, focusing on needs, your own as well as those of the people with whom you communicate.
As far as exploring your own issues around this, I would recommend some counselling, if funds allow it. It is such a great thing to do, even if you just decide to have a very limited number of sessions. For me, much of my adult life has been about creating a kind and supportive narrative 'in my head', if that makes sense, and counselling has contributed to that.
Also, sites such as www.handinhandparenting.org/instructor_location/uk/
offers affirmative and supportive advice and insights without being preachy or judgmental.