Mother - actually, yes. My son. I was also bullied as a child, in senior school, by my peers. Not online, because that didn't exist at the time, but in person, with fists and shoves in the back going up and down flights of concrete steps. I know how it feels on both counts.
The key difference between you and the adult who has threatened to physically harm the OP's child is very simple. You may have thought it. You may have felt it. But you wouldn't, and didn't, do it.
There's a very old adage, which I'm pretty sure that you know: two wrongs don't make a right. You know that. I know that. Even the garden gatepost knows that. But does the adult who felt it appropriate to call a 13 year old child a cunt and threaten to physically hurt her if they see her, know that? Or are they just as much of a bully as the OP's daughter? Worse than the child, in fact, because they are an adult, and a parent, and ought to know better...
I'm sorry if my post offended you. And I am incredibly sorry that your child was bullied to such an extent. When I was 14, I tried to kill myself to get away from my so-called "best friends" at school and their bullying (low-level, so that the teachers wouldn't pick up on it at school, then they'd step it up outside by turning up on my doorstep and saying that I'd invited them round - I was too terrified to say that I hadn't, that I wouldn't, what they were doing to me, until my oldest brother walked into my room one day and caught one of them trying to set my hair on fire as I tried to fend her off). I ended up in hospital overnight, and had a brisk chat from an Army doctor about how I really needed to "pull [myself] together and stop worrying my poor parents". That was a year before the incident with the lighter which my brother walked in on. I'm also in recovery for an eating disorder. I'm not sure if the behaviour/triggers for the ED ever go away fully, and I don't know if this will be any help to you, as a worried mum with a child still enduring what happened to her three years ago, but you're doing the right thing. Please believe me on that. From someone who has been both where your child was (albeit many moons ago), and where you are as a mother, you are doing the right thing. And one day, hopefully soon, it will get easier for your child. I'm sorry. 
OP - the only thing I can suggest is that the next time she physically hurts, or threatens to hurt you and/or her sisters, dial 999. Children's Services will have to do something about the situation then. And your husband will have to stop enabling your daughter's behaviour... hopefully before it escalates. Because it will. You know it will. Your other children need you to step up and be a parent to them, as well as to their sister. My daughter was an adult when she was first arrested - and the police couldn't have been more helpful. They pushed for her to have MH intervention (our GP refused to help, even though I was showing her the bruises on my body and sobbing, begging for help... when my daughter was 14 or 15 years old, so I get the lack of comprehension when it comes to such things, in such quarters), because they could see I was at my wits' end with her behaviour/attitude/lying. Children's Services also were extremely helpful, and understood that my son was/is safe around her, as am I, as long as she takes her medication and remains on a stable playing field. As she's an adult, though, obviously I cannot enforce that. The last three times she's been arrested, however, have been because of her behaviour to other people outside of the immediate family. And because of this? She is at risk of being thrown off her uni course (not allowed to return for her 3rd year, which means she won't have a degree), and completely screwing up the future which she has always dreamed of. As her mother, I can't help but wonder if I'd dialled 999 a few years earlier, she would have received the help sooner, and not be in this situation of her own making.
But please take that parents actual threat (not simply felt, or thought, as Mother - and so many others, I'm sure - has admitted to experiencing) seriously. Yes, what your daughter has done (or admitted to doing, and I'm willing to bet - if she's anything like my daughter was/is - that there's an awful lot more which you don't yet know about) is disgusting, but adults cannot simply go around threatening to beat children up! Irregardless of what that child may or may not have done to that adult's child.
Feel free to PM me, though, if you want. Because being caught between a rock and a hard place is neither easy, nor fun, is it?