I have the same issue with my boyfriend's daughter, 11. Resentment towards her simply because she is here sometimes. She is very much strong willed and has NO problems telling me that I'm not her mom that she doesn't have to listen to me...unlike your situation, my boyfriend's discipline techniques are opposite from yours, I'm the stand your ground parent, he is the benefit of the doubt do ruffle feathers parent.
I feel like when I'm being disrespected by his daughter, I'm also being disrespected by him, simply because of the fact that he CHOOSES to do nothing (or very little) to fix the problem.
I have gone out of my way to become a "friend" to his daughter...but my attempts at showing her any affection, love or acceptance...lead her towards searching for, yet again, the "negative attention."
Between the two of us we have 8 children. We came up with a chore sheet and a consequence sheet, agreed upon it and the discipline is clear and consistent...that has seemed to work some..there are the "discussions" about it, but over all that has worked for us. Maybe try something like that. I wish you luck.