The trouble with a forum like this is we only get a snapshot of a situation. OPs of threads are possibly unreliable narrators. We add on our own prejudices and compare our very different lives and what is left are kneejerk reactions.
Obviously OP has done an awful thing attacking her daughter and there's no justification for it.
However, we don't know that OP is, in general "an abuser". Today she has done something that is clearly abusive - but we don't know whether this is part of a continuing pattern of abusive behaviour or whether it was one off uncharacteristic behaviour. Obviously this family needs help to unpack this and stop this happening again, but the action that needs taking really depends on what has led up to this point.
Maybe OP has a history of exhibiting abusive behaviour to her children and this is why her family feel like a united front against her.
Maybe OP is a mentally unwell person that is being emotionally abused by her husband, he's been playing the children off against her for years, her older daughter is picking up on the husband's behaviour leading to OP feeling more bullied, and today has been the straw that broke the camel's back.
Maybe neither of the above scenarios reflect what has really happened and it's a different story entirely.
I don't think right now us attacking the OP or exonerating the OP are helpful. We don't know what's at play here and why this has happened.
I also think, OP, that all the "awful mother" stuff is unhelpful in evaluating what is going on and what needs to be done. It's very easy to hide behind berating yourself and calling yourself names - it's a way of thinking you're punishing yourself and therefore taking accountability, but really you're hiding under a mountain of self pity. You may deserve pity, I don't know, but now is not the time to indulge in this. It's not addressing what the problem is and finding a solution.
Right now, OP, I think you need to get some breathing space between you and your family Is there anywhere you could stay today - even a hotel if there are no friends and family - and then tomorrow get to your GP, have a very honest talk, and to try and get the ball rolling on some support for you and your family.