Welcome to the board. I'm glad you've found us. You've been given some great advice so far.
I have a question. You have Borderline (BPD) listed as one of your difficult child's dxs. Normally, that's Borderline Personality Disorder which isn't generally diagnosis'd until adulthood. Did you mean Bipolar (BiPolar (BP)) instead? If that's the case and your difficult child is on a stimulant without a mood stabilizer, I would imagine you are seeing a lot of aggression.
My difficult child is 12, also, and lacks emotional regulation. I have found that picking my battles is an absolute necessity. In fact, we only work on one thing at a time. Otherwise, my difficult child becomes too overwhelmed and meltdown/rage ensues.
From what you've said, your difficult child has had a traumatic childhood and is now having to adjust to a new home with a new family. That has to be incredibly rough for her.