I'm not defending your DSD and I'm sure it's very hurtful but try to remember that she is still a child and is at a very awkward age, with hormones raging and swinging between feeling like an adult and a child. I was a NIGHTMARE that age and can recall telling my step father, who would have moved heaven and earth for me "you're not my Dad and never will be!" all the time when I was annoyed. I am horrified now at how hurtful that must have been but at the time I was angry and lashing out.
I have a DSD who is 12 and we have an element of veering from one thing to the other. One minute she loves me, wishes I was her Mum and wants to do hair and make up together and then, when asked to do something she hates it here and wants to go home where it's "more fun" so I do know how hurtful it is.
It is a very real possibility that she does feel pushed out by you and maybe a bit jealous of your LO's who have both their parents living together all the time. It's not something you can change, but sometimes just acknowledging that they feel that way and letting them know those feelings, while hurtful, are perfectly normal, might help.
I agree that she needs to work on the relationship with her Dad - do they have a hobby or interest in common or could they develp one? Perhaps he can have time time once a week where he just does somethig with his older girls such as bowling or ice skating.
I think you need to step back a little and let the Dad and the girls sort it out, while perhaps reassuring them that you love and care about them and will always be there for them if they want you to. When my SD is lashing out I tell her that I understand she is angry but that I love her unconditionally, even when she feels she doesn't like or love me back. I find a lot of her outbursts are about testing out how me and her Dad feel about her - if she says she wants to go home, will we just cave in and take her or do we let her know how much we would miss her if she wasn't with us for the week end. The latter is what she wants to hear of course and sometimes it's just reassurance of their standing in the family that they need.
I'm not saying it's easy though - sometimes it hurts like hell!!!