As a step-parent, I sympathise.
If you have problems with your step-daughter because she plays you off against her dad - don't worry, ALL kids do that, with natural parents as well (I have a daughter with my wife as well as her two children from her first marriage) - but it feels worse as a step-parent.
If this is an issue - talk to him. You need to produce a united front to her - ensure that you back each other - even if you think the other is wrong (and he will get it wrong too!)
Back that up with a lot of patience and love. It's tricky for a girl this age to be in this situation.
Do NOT try to be her friend - it won't work, and she will not respect you.
Make sure that she knows you and her dad love each other - and her - and that you are all a family together, which includes everyone being nice to each other.
Try and have some one-to-one time with her - p[ics or even just a DVD. Don't force the conversation, but let her know she can chat to you - occasional chatter revreals something deeper, that's the way children work.
It's not easy, but if you are patient while she tries out the boundaries, she will eventually accept you. You are not her mum, and neither of you are going to pretend that you are, but you are her dad's partner, and she needs to accept that - and you.
Finally - make sure he agrees with his ex that none of you will ever fight over this child - again she will play you all off - so make it a rule not to make her a weapon between you.
Complicated isn't it? But worth it in the end, I promise.
If you need some more advise, do post again - lots of wise heads on here!