Hi, I'd like to help you with your question.
This news had to be a shock for you. I am sorry to hear you have to go through this.
It is going to be hard to determine if your husband is telling the truth about the situation. You can make it known to him that doing so is in the best interest of the marriage and for him as well, but that doesn't guarantee he will be forthright.
It is a hard decision to make, whether or not to stay in a marriage like this. I think there are a couple of ways to look at this:
One, if you stay, the two of you would definitely need to see a counselor. The feelings that your husband's actions have caused for you as well as his issues with molestation must be resolved before you can consider moving on.
You also need to address how you feel about the situation. On one hand, you have your feelings about what he did. On the other you have your feelings about your daughter and the effect of the molestation had on her. And third, you have your feelings about your marriage and your husband. There also is probably some grief involved because of the loss of the image you had of what your marriage and husband were and the loss your daughter suffered. You also have your husband's alcohol use on top of that. He needs to become sober and deal with his use.
Two, you can leave the marriage. Leaving would help you heal in that it separates you from your husband and helps that you don't have to face him each day. But it also means that after 32 years you would be alone. There also would probably be grief as a result of the loss of your marriage. That may be the biggest loss and would take some time to get through. And if you decide to divorce, there are financial concerns as well.
There are some resources that may help you. No matter what you decide, counseling is needed. You need support right now, either way, and a therapist can help you. Ask your doctor for a referral or if you attend church, your pastor could help. You can also find a therapist on line at http://www.find-a-therapist.com/.
You may also want to consider getting help for yourself so you can better deal with your husband's drinking. Try this link- http://www.al-anon.alateen.org/. There are also support groups you could attend.
There are also some books that may help. One is called Addict In The Family: Stories of Loss, Hope, and Recovery. by Beverly Conyers. Another is When Your Child Has Been Molested: A Parents' Guide to Healing and Recovery by Kathryn Brohl and Joyce Case Potter. These are available on Amazon.com or your local library may have them for you.
I hope this has helped you,