maybe she is just doing what she is getting away with
How many 9yos actually want to hurt the people they depend on and smash up their own precious possessions? How many 9yos would even think of trying that out if they thought no one would stop them?
Autism has been mentioned and that is a possibility. There are other possibilities too. I have had 2 children with similar behaviour patterns in my family: in one case it was a question of adoption trauma, in the other of severe and probably inherited anxiety coupled with PTSD.
In both cases, there are happy endings, in that both children grew up into lovely and self-controlled adults with no issues around violence at all. It has to be said though that the child with anxiety did need therapy and is still as a young adult on medication. CAHMS recognised that she had a chronic mental health condition and that she will probably always have to manage her life around it.
The first child was my sibling, the second my daughter. Both had to be gently restrained at the time because they had siblings who had to be protected and because we felt as parents that it would be very bad for them too if they seriously hurt a parent (besides, parents are people...)
Both had parents with very firm boundaries who expected and usually got obedience. My db was the sweetest little boy, beautiful manners, very loving and considerate- and then he had his bad days.
Dd again was the most affectionate child you could meet, and we were probably that little bit stricter than some of her friends' parents, but also, I think, more consistent.
What I used to do was to hold dd from behind while repeating gently and calmly No, I am not going to let you hurt anyone, No, I can't let you hurt anyone. She needed to feel that her house was one where no one must be hurt, and that I both had the will and the power to ensure that.
Behaviour charts never worked because they just piled on more anxiety. Punishment afterwards never helped either and I didn't feel it was fair, any more than it would have been fair to punish someone with a high fever for lashing out in a delirium. Many years later she told me that during these meltdowns she felt like she couldn't recognise us, that I was just some monster that she had to defend herself against.
She always behaved perfectly at school: that was also part of the anxiety. In fact, she put up with some horrendous treatment there because she was so anxious. It all came out at home.
It's not bloody autism as it would continue outside the home too.
Do you know many autistic children? They often exhaust themselves masking while outside the home and then lose it when they get back, exhausted.
With children suffering from anxiety this also applies.
Of course we can't know for sure if the OP's dd has an underlying problem or if this is learnt behaviour. But from my experience there is absolutely nothing that rules out an underlying problem, certainly how she behaves at school has nothing to do with it.