Ok there is quite a lot to unpick here and I feel some of the responses aren't looking at this situation holistically.
Assaulting your child, wherever their age or provocation is not acceptable. It's a criminal act and one the OP needs to take responsibility for.
The positive here is that the OP accepts she is in the wrong. She is remorseful. Has apologised and is seeking counselling.
Like many others I do think some time away from the family home would be beneficial to give everyone a chance to reflect not only on the event but the wider dynamic within the family.
However the other serious considerations here are the OP's ongoing MH concerns and the lack of support from her husband.
She is the person who hit her child, but simultaneously her DH has spent years undermining her and pitching himself against his wife.
Being the "fun parent" really means not parenting at all but he's worse than that in actively enabling his daughter's poor behaviour.
He is not without blame here (under said) and it's perfectly reasonable to hold this view whilst simultaneously being clear that the OP's behaviour was appalling.
I'm also somewhat surprised by people suggesting the daughter's behaviour is normal for a teenager.
I'm not so concerned about a messy room or an accident with a burnt carpet but it's beyond that isn't it. Broken beds and mirrors, causing a major leak and the constant "shhh" and lack of respect for her mother is awful and no, I would not accept or tolerate this.
Yet the OP has to become her DH provides no backup whatsoever and seeks to alienate her within the family.
I don't condone the OP's actions but I do feel sympathy for her.
It's also why I think she needs to leave the home not just for her daughter but for herself.
Her husband needs to understand that he needs to parent and live with the consequences of his actions. I wonder how long he'll stay being Mr Fun if the OP is not there to provide any boundaries whatsoever.
The whole family situation is toxic and both parents are at fault, the OP for remaining in this situation but the DH certainly for creating it.
The children (and daughter especially) will be traumatised by what has happened but they will also be impacted by the longer term dynamic of seeing their fathers ongoing poor treatment of their mother and normalising this - and I don't underestimate the negative consequences of either of these abuses in their development.