You've been very good to admit this EB, and I want to try to help. I think taking on step-children is a remarkably difficult thing to do, I found it very hard 12 years ago, and sometimes dh's commitment to seeing his kids still causes me to feel a bit resentful, even tho' I fully support his involvement in their lives.
You know what, I think you're jealous. Like many emotions (including love and hate) you can't help it, but you have to try to conquer it, for the sake of your relationship, as well as for this little girl.
She causes your dp to see his ex twice a week, and you don't like it, and she is your dp's little girl, and while she's around you are not the centre of his world. Analyse your feelings, I'm right aren't I?
Does your dp know how you feel? Can you talk to him about it calmly? if so try to talk it out.
I MADE myself spend 1 to 1 time with my stepdaughter when she was little and that helped me get over my feelings a little, cos I got to know her rather than 'what she was'. Now she's 16, we're pretty good friends.
I hope you're not upset by what I've said. Can we talk more about this?
One more thing, how do your children get on with her. Don't let them see your feelings towards her please, she needs friends at your home you know.