Her father's the root of her problems. In her *child's* eye, he's the one who caused her this grief. Of course, she doesn't see that maybe he's better off divorced from her mother, happier with you, etc . . . but that's an adult's understanding, not a child's. You can "tough love" her to death. The child has a spirit, a soul, a need to feel loved, and for whatever reason, in the tangled mess of a divorce, that came apart for her, and she is insecure, uncertain, scared. Scared children act just like scared animals. Yes, she does need structure so that she can cling to something, feel in control. . . but she also needs a certain kind of attention to let her know she's special. Her dad helping her with her homework must feel frustrating to her. That's just general and she must know he's "obliged" to do that. Kids are smart.
Do something special for her to make her feel special. Take her iceskating and let her know she's great at it. Have dinner with her and ask her what she's feeling, what sorts of things she likes besides school. See if she'll let you take her to a museum or bookstore - just her.
The more everyone fights her and treats her like the "difficult child" you called her in your post title, the more she'll continue to act out.