Mumoftwomonsters I think you need to make it plain that she's always welcome in the family home but that her behaviour will not be tolerated, any more than it would from any other member of the family. That being part of a family is about reciprocal responsibility - a two-way street. She has no right to act in such a rude and histrionic way and if she has a problem, the sensible and polite thing is to sit down and talk it through. Not to be spiteful and aggressive.
It does occur to me that she is old enough to understand the idea of infidelity in a more immediate way than when she was younger, but lacks the life experience to understand how complicated things can be. So she may really be struggling with affection for someone who she knows her father slept with, while with her mother, in a way she never did when younger. Has she a boyfriend now, maybe? Sexual jealousy is very much worse than any imagination could make it and if she now understands it, perhaps her anger comes from that new knowledge? It also occurs as another option that kids do feel rejected when a parent leaves, and perhaps she is finally pushing your DH to see just how much he does, actually, care. For this reason I think he needs to care enough to stress that she is always welcome in your home, but that he also cares enough that he is not going to let her get away with crap. Because taking the trouble to discipline your kids is a form of caring. It takes emotional effort.
I know foster carers say that kids who have suffered in early childhood often seem fine until they hit adolescence, whereupon it all goes horribly wrong. Was the split very traumatic?
I do really admire the way you've tried to meld everyone into a united family. My step-mother number 1 was vile; she once rung me to explain that the family was her, her husband (aka my dad!) and their kids and I was not a member of that family, and that he'd promised her he'd have nothing to do with us, and was breaking that promise and she was very angry that he was breaking that promise. She'd met me once before at that point - and I'd been pleasant! So Dittany can can it, frankly: I know bad step-parenting and this ain't it! You sound far more like my 2nd, fab one, whose side I was on when he left for the third (yeah, my dad is a cretin). Arranging 1-2-1 time for him with the older girls, inviting their mother over, treating them as one family... sounds pretty damn good to me. She's lucky, and I don't think this is about you. It's about her.
I think her dad needs to sit her down and talk it all through. She has issues, and you may well just be the scapegoat.