I've got a special blended situation going on here, too, so I feel your pain.
Question: Are you and your BF planning to marry? I'm not judging, but I wonder what the kids have been taught about marriage. When I was dating my husband, his XW emphasized to all, including their son, that I was merely the girlfriend and, therefore, of no consequence. (Now that we're married, I'm a bad habit--addiction, maybe--that he's forcing them to put up with.) How long have you been together? How long have you been in their lives? If he's "newly divorced", then this is certainly a new concept for him and for his children (sharing each other like this, with "outsiders"), not to mention a new set of circumstances in that their parents are divorced. They're all--the children and your BF--still dealing with the dissolution of life as they knew it, and they all need space to get it together. (He might act like he's fine when it's just the two of you or even with your children; but his children's presence reminds him of the mess that he's made in rocking his and their existence, even if it was a terrible marriage.) Is it possible that this new live-in situation is premature? If your children live with you and your SKs' father all the time, then there's definitely resentment and even rage that he went from living with them to being full-time head of somebody else's family, spending day in and day out with someone else's children who are the same age, feeling to them like a quick replacement. Don't think that just because she's the only one acting out it means that she's the only one with a problem. Because she's "favored", she feels more confidence and more obligation to fight for herself and her siblings.
Now, you and BF need to get together and establish the house rules (including an understanding between you of the purpose and goal of each rule). You need to discuss parenting styles and how you will address the differences between you--if you will have equal rights to each other's children or if each bio will step in and pull rank over the step. Once you establish how your home will run, then you both must work together to ensure that it happens.
I really suggest counseling to provide guidance and perspective, as I don't see your relationship with your BF succeeding without coming to some major agreements here. You have no right to expect a ready-made family at this time, so don't try to force it. You can't expect them to come over and fall right in line with what you do in "your" family, when they feel like their dad is their only family there. No matter what you do, it will get worse before it gets better.
I wish you all the best.