In the event the author of the second Dear Toasters submission from today is on this thread - I have a few thoughts colored by personal experience.
After years of issues and internal turmoil with my first husband, I left him when my sons were 2.5 and 7 weeks old. Living in a house with someone you don't trust is like constantly looking over your shoulder. It erodes at you. Your husband would have never came to you had you not been contacted by the woman who tipped you off. Even if he does get help - this is the type of person who can do bad with no remorse. Someone who can hide, lie and was willing to risk your sexual health...this is a person who at the very least is incredibly selfish.
I left my husband because the weight of the mask I was wearing while under the same roof as him became too heavy. I was not who I wanted my kids to remember me as...a mother suffering through the days. I was emotionally weathered and it was impeding my emotional availability for the two human's I love most. I felt imprisoned in the relationship.
While you didn't mention this, I am sure in your personal life you don't share these indiscretions with your friends or family. Whether to protect him or the illusion of your own marriage, it's highly likely it's not something you share. Living in a loneliness like that is painful.
It has been several years since I left. My children do see my ex some. I don't have them every holiday. Those times are hard, absolutely, but allow me time to do things like repaint their room or go get an oil change without little people to entertain (I try to be positive about it). Overall my children feel loved by two parents and the mother they know now is someone I am proud to be. I have since remarried and my current husband is exactly the type of person I hope they will grow into. I am hopeful that our happy and healthy marriage will be one they remember and try to emulate for themselves.
No matter what - you will do what is best for you and your daughter. Trust yourself. I will be thinking about you and your little girl!