OP, here's a bit of perspective from the other side.
My SM has been very hostile to me at times, in very similar terms to the ones you've used to describe your DP's daughter. She has said she experiences me as manipulative, cold, unfriendly and hostile to her.
From where I was sitting, I was reserving judgement until I knew her a bit better. I was happy that dad had found someeone, but wanted to hold off from being all gushy and 'we're BFFs now'-ish until I had more of a sense of who she was. She interpreted that as mean, cold and hostile, the fights kicked off, it's unlikely that we'll ever be on more than chilly and formal terms now.
I suspect that stepmother/stepdaughter relationships are particularly fraught, perhaps because there's an element of competition: daddy's girl vs daddy's girlfriend. Your stepdaughter is also approaching puberty, which will kick that up another 18,000 gears.
I really wanted my SM to make an effort, get to know me, in effect win me over. She thought I should automatically love her, and kicked off with tantrums and name-calling when I didn't.
My circs were a bit different, as I was in my twenties when dad remarried. In this case you're the adult, and I'm afraid it's up to you to try and win this girl over. Please try and win her over. She's part of your DP's life just as you are, and I would hate for you to end up abandoning your relationship, or destroying a troubled adolescent's relationship with her Dad, just because you can't be the bigger person.