This is a child who has clearly emotional issues and understandably so. A mother who abused her emotionally to the point she wants nothing to do with her anymore, but yet battling with the fact that deep inside, she still loves her, and therefore probably miss her love desperately.
A father who she's never bonded with, who is looking after her, but who she probably doesn't feel close to as a daughter and father normally do. She senses that he doesn't know how to deal with her emotional need and that makes her even more threatened to let her love him.
Then there is you, probably the only person who showed her unconditional love and who she probably feels closer to loving healthily, except that you are her step-ups and as such, possibly not a constant in her life. So she tests you, not even willingly, she probably kicks herself when she upsets you, but something makes her do it, just to see if you'll still love her and be there for her, even when she is horrible.
This is so typical of children who've been raised by unemotionally involved parents. They are extremely demanding emotionally and very hard to deal with by the people who become close to them. It is not surprising you are finding overwhelming. I sense from your posts that you don't blame her, you are just exhausted from holding her up.
I understand that it must be hard for your husband, but it is ultimately his responsibility to try to build that father-daughter bond with her and learn to take on the emotional overload. She needs undivided emotional attention.
Ideally, she'll meet someone who will be her rock, but it is a very scary prospect for a young man and she is therefore attracting the wrong ones, those who make promises and then let's her down.
I can relate to a much lesser degree to what she's been through and what 'saved' me was having my daughter. I waited until I was 29, stabled and more mature, thankfully, but the moment I held her, I knew I could love unconditionally for the first time because I knew that if I was a good mum to her, she wouldn't run away from me or push me away. The weight that came off my shoulder the day she was born in undescribable.
It might be extremely tough OP, but you will get the rewards because deep inside, she is probably a great person, and when she becomes more emotionally stable, she will finally show her gratitude towards you for being the only adult who went beyond to be there for her.