First of all, let me preface my comments by saying that I used to be a licensed professional counselor specializing in child and family therapy. I worked at three different residential facilities treating troubled kids, and I also headed up an outpatient program for the same. I have seen the worst family dynamics and heard the most horrible stories that you can possibly imagine.
That being said, one thing that I had to learn early on in my career is that you can not FORCE a child to give up on his or her parent. No matter how big a scumbag Mom or Dad is, the child will still crave his or her attention and approval. Even if the child berates the parent him/herself, he/she is likely to turn on anyone else who joins in. While you would certainly be well within your rights (and I imagine the court would agree) to restrict your daughter's visitation with her mother, you will need to prepare yourself for the potential consequences of doing so. In a worst-case scenario, your daughter could displace all of her anger and resentment onto you, thus making you "the bad guy" and preventing her from confronting the real source of her angst (Mom). As a father myself, I can appreciate your desire to shield your daughter from any and all pain. However, there are some unpleasant things in life that we all DO need to experience, as this is how we learn and grow.
In the end, you must choose the course of action that's best for your daughter, and only you can decide what that actually is. In the meantime, be prepared to listen, choose your words carefully, withhold judgment, and (here's the hardest part) avoid giving advice or telling your daughter how she SHOULD feel. I applaud your willingness to seek counsel for you both. This is a sign of true strength, and not weakness. Best of luck to both of you.