I'm so sorry you and your family are struggling with this
I am also a therapist and I have to say, I feel you are doing everything right with your approach. So, my thought is actually that she needs some help with her liver and/or detox. I know there is a lot around this but I highly recommend you see a Functional Med Doctor who can help with this.
We had this issue with both our son and daughter. We lowered their inflammation and detoxed them and it has made a world of difference. When a child is that angry it can be a reflection of a sluggish liver or a body that is having a hard time detoxing on its own. The inflammation can also be happening in the brain causing some rage.
Here is who I highly recommend: Theresa Hernandez at Family First Functional Medicine.
https://familyfirstfunctionalmedicine.com
*If you mention my name and tell your story Theresa will understand what I have explained here as she has treated almost everyone in our family.
It is absolutely an investment to go this route but the peace we have in our family now is worth every penny