It's so hard with kids, girls especially (i think) because this is a crucial time for them. While they will get influenced by outside sources, Mom and Dad are the primary teachers of basic life skills.
I'm sure your W treats D like a friend. She needs her on her side. D is going to be more inclined to want that. My dad did this with my sister and she really struggled with it, still does a little. Now, she hardly speaks with him because she can see (now that she's older) what was happening. You are probably trying to teach her to be responsible and I can't think of any 11YO that wants that. Definately keep doing what your doing in that regard. w is hurting D by doing what she's doing, so at least you need to be a good dad, like you are.
You might look into the counseling for D. I don't think she will resent you for it if you can make it fun for her. Find a woman, someone fairly young, a place that works primarily with children, so it is kid friendly. When i was younger my C had me draw pictures rather than talk sometimes. I know you don't want to bribe her, but maybe something like saying that after the C you all could go get some icecream or something. Think of it as rewarding positive behavior more than a bribe.
If i can't fall in love... I'd like to fall in chocolate! ~ Author Unknown
