I think the answer to this is family counselling.
If your daughter has suggested staying at her father's more, then maybe allow it for a while. It does no harm to show you respect her choices - but if he's as useless as you say he is, she'll soon realise the grass isn't any greener at dad's. Once she accepts there isn't any easy way out of her now blended family, she may be more willing to engage with the family counselling. I'd let her try it her way for a while.
I would, however, insist on the family counselling anyway. Tell her this is a big decision and it saddens you. Tell you want to respect her feelings, but DH and the step siblings aren't going anywhere, and it's not feasible for her to just drop out of the family and avoid them like this. Ten is still quite young - there may be a part of her that thinks your new marriage won't last, and you'll get back together with her dad. You may think she's too mature to think such a thing, but you'd be surprised the secret hopes children can have. It may even be something she's doing subconsciously. She could be holding herself back from warming to her SS, because if she welcomes them in fully, that makes this new family configuration permanent. And part of her isn't ready to accept that.
I'm sure your daughter is a lovely girl, and I'm sympathetic to her being a sensitive girl and wanting her own space. But growing up, she has to learn to balance those facets of herself, to have relationships with others. Not everyone is going to be as accommodating to her desires as her mum. Does she struggle with friendships in general? From the way you talk, it seems like the problems are all emanating from DD? That the step siblings would be happy to all be friends, but she feels triggered by them being around at all? If that's the case, then compromise is the solution here. Everyone needs to do the work and change a little, to become comfortable with everyone else. DSD needs to learn to dial it down a little for DD, and DD needs to learn a little more resilience, to become more comfortable around DSD.
It's not just going to fall into place, but I really think this is your only option here. The suggestions of not living with your own husband, or leaving him altogether, are obviously not going to happen. So family therapy for all four of you is your only real hope. You need an outsider who can see how you're all interacting with each other, and hand-hold you through the discomfort of change.