Some solutions just can't be found without professional help, and I think consulting a skilled child psychologist who comes well-recommended would be a good start. The difficulties with your exAH are going to intensify, and the marriage counselor you have consulted may not have the necessary training to be able to advise you about how to support your child during the crises that likely are ahead in your exAH's future.
Your child will be reluctant to be honest with you about her experience of her father. She will also be confused at times in her experiences of you. But a skilled professional can spend time with her in session and can assess what is really happening, what she really needs, and how you can respond in a healthy way.
I don't think we do very well with these potent, complex alcoholic family issues on our own. Our perspective is often distorted, we often are in denial and see only what we consciously allow ourselves to see, and we often do not have all the information we need. In addition, if we are recovering from trauma, we may become even more ill from the stress of wanting to do what is right for our children--and not knowing what that is.
If you have medical insurance, I suggest you see your family doctor, explain the need for a referral (a "prescription for therapy") to a child psychologist, and perhaps the necessary sessions will be covered so you will not have to pay a great amount out of pocket.
So many parents on these forums feel tremendous regret that they did not take a course of action that could have made a real difference in their children's suffering within the family of addiction. Often they wish they had gotten professional help for their children and for their own parenting challenges.
Your husband is dangerous to your child's emotional and psychological well-being. But a professional will know how to counter much of the potential damage. I would not personally rely on any advice other than from a skilled professional.