I haven’t read the thread fully but I have read all the OP.
this was very much like my DD now 7. I also came from an angry household and have had to really work on my own anger.
a couple of things to consider that might relate.
with my DD it has become completely clear that her blood sugar rules her moods. And she’s very picky and hard to feed. After a meal you have about an hour before she dips again- so we found frequent snacking makes a huge difference. We are trying to get a referral to explore pre diabetes as a cause.
we also realised that setting strong boundaries helped a lot, but we had to be super careful about language. She was really internalising the idea that she was a bad kid- ‘stop being naughty’. She responds so much better to ‘not putting your socks on is not good behaviour, what mummy would like you to do is put them on without shouting, now. If you don’t put your socks on mummy is going to count to 3, at three you’ll lose some tv time later’ but really calmly. If she does the good behaviour, lots of praise ‘well done that was great behaviour’, and if she hit 3, ‘ok you’ve lost tv time, but you can get it back if you do x really nicely’- the formula is, name the bad behaviour, set out clearly a good alternative. Propose sanction, follow through on it but always allow a route to undo the sanction. Reinforce that you love them but not the action.
when the situation is resolved taking time to say ‘sorry mummy got cross, but I’m not angry at you, just at your behaviour. You are a good kid, we just need to work on doing things when mummy asks etc.
on top of this I have to accept that still she needs help getting dressed, and it’s better for us to gently help her than to leave her to her own, if that eventually leads to me losing my temper and shouting.
we also say to her, we don’t like days when there’s shouting, it makes us all sad, so let’s work together to shout less.
always apologise for shouting or losing your temper. That means she learns to do the same when she loses it.
i think with my DD over time she came to feel that she wasn’t very loved, and we really had to unpick that and rebuild trust, her behaviour and our bond is SO MUCH better now.
we did have to asses everything we were doing and recognise none of it was really working, and go back to scratch.
lastly- the part about growing up in an angry family. For me, I was definitely struggling with anger that was related to my stuff (issues with my parents or work) that I couldn’t properly allow myself to feel or express was sometimes being expressed at my DD and she fundamentally could read that, and I think felt a bit unloved, and also had a deep sense of unfair treatment which was making her angry and really badly behaved. I had some therapy to help me understand the things that were really making me deeply angry, and now that is more in awareness I basically don’t get cross or angry with my kids in the same way at all. It’s been super helpful.
no idea if thats relevant here but just in case! Good luck x