Write her a very short card stating that you love her, that wherever she chooses to live, whatever she decides to do you love her deeply and believe in her.
That you will always love her, and your door will always be open and will be waiting for her when she is ready.
Give it to her, with a small necklace, an angel or guardian to look out for her.
Mean every word, if she gets in contact, leave the past behind don't speak about it again, and embrace her wholeheartedly. In time when he trust has returned you can get some help for her.
This poor girl has been damaged I suspect by the abusive relationship you have had with her father. Somewhere along the line your relationship with her has broken down - for reasons perhaps you do know in your heart, and this is the outcome, and it is very serious.
Personally in your position. I would organise for the other children to be looked after, and I would take her away just you and her for a few days, walk along the beach and look her in the eye and tell her how much she means to you, that you are sorry for her terrible childhood and you will do all you can to support her. You need to try and reconnect with her.
I am not blaming you for your terrible ex, and his abuse, but you are safe away from him now and your dd is now in peril.
Have you got a grandparents that could get involved?
Other family members or friends?
You need some proper support op. I would call SS again and tell them you think she is in danger with her father. I am surprised the school have not already contacted them.
Family counselling would help, if she would agree to it.
Do everything possible - throw everything at it - and try and get her to see how much she means to you and her life does have value. SHE has value to all of you no matter how badly she behaves. Given her situation her behaviour is not surprising at all. It will pass as she gets older, and finds strategies to deal with her sadness, confusion and trauma, but right now she is in the eye of the storm, and you need to be right there with her - everyone else's needs are secondary to getting her through this. If the worst happens, the fall out will be absolutely enormous for all of you - including your younger children. So I simply do not agree with pp that say put yourself first. Not in this incidence do you put yourself first - she has to come first until she is in a a place of safety both physically and mentally.
I wish you all the luck and love in the world. Go and get your girl op, find a way. Keep banging down those doors, if nothing else she will know how much you care, it will count for something on some level trust me (as a dd that slammed the door on my own mother more times than I can count) It WILL get better, but you need to get her to a place of safety.