What a horrific situation
My 12 yr old son is really a rough kid to love sometimes, because of everything he has been through. I could go on for hours about all the trouble he has caused out of hurt, anger, resentment, bad behavior modeling, etc.
Going by what you have said in your previous posts, you and your DH are the only TRUE positive influence in this poor little girl's life. I let my son decide which parent he wanted to be with, when he was probably 8 years old. He chose to stay with his dad, so I let him go out there for the summer (with some visitation). It was the biggest mistake I ever made. At 12 years old, he still ripple effects from it. Being with his dad and not seeing me for longer periods of time took away the good influence in his life to balance out the bad and things really went to heck. She may be acting aggressively and lying a lot (btdt!) but she just has to be hurt and confused under it all. They say that anger is a symptom of another emotion, more than an emotion unto itself, and I truly believe that.
I'm not sure what the situation is, that your husband has all these hoops to jump through in order to see his daughter. I can understand no spanking, maybe things like time limits, bedtimes, just general parenting "stuff", but there is NO WAY she has a right to deny them counseling.
I would like to tell you what I would do. Please don't take it as a lack of sympathy for what you are goiing through, because I really really feel for you.
I would encourage my DH to tell his daughter that he is not giving up on her, that he will NEVER give up on her, and that he loves her and she is a part of him. (not speaking of technical arrangements, but the feeling that she is a part of his life and is important to him really might be an issue for her...especially if there's a nasty ex whispering bad things in her ear) Then, I would take the lawyer stuff, and turn it around. I'm sure that the court would love to hear the list of stipulations made that include not seeking family counseling. The court can force counceling, and I think that the daughter really REALLY needs it to make sense of the crazyness that is going on right now. They need counceling (the daughter and your husband), you all need family counceling. Its tough dealing with a kid who is so frustrating and seems so angry and vindictive, and trying to understand whats behind that feeling might make life a little better for you all.
So, if it was me, after forcing the counceling issue, if those involved all still think its in the child's best interest to go with mom completely, I would step back and allow it to happen (again making sure she knows that no matter how much of a brat she is, you all still love her and will be there when she is ready to be a part of it again) I don't think my son could make the decision about who he wanted to live with completely on his own, but I do think that he would be a welcome part of the decision making process.
In the best world, you could all sit down together, mom, dad, step mom, daughter, and discuss it and come up with a good solution, but unfortunately it seems like the only way this could happen is if you used your court time to get a mediator, to help with the conversation.
I hope it works out for you all, no matter how it ends. I feel for you.
My DH feels for you too (as a step dad to a very unusual child, he has a lot of the same frustration issues that you do, with our son not functioning "as he should". we're just lucky that we don't have the outside influences that you have to deal with, anymore)