Hope... the two aren't intertwined necessarily... You don't trust him, clearly, but guess what... you have a d together. So you will have an r with this man for many years to come. Just because you divorce him doesn't end that.
The trust issue is going to have more to do with forgiveness than a legal piece of paper declaring a divorce. If you divorced him today and asked him to keep OW away from your daughter, would you trust that he would do that? If he violated that trust would it bother you? So now you'd be divorced and still not trusting him.
I'm not saying to not file or to file... I'm suggesting that filing and trust really don't have a direct relationship. If you want to trust him again you will need to find a way to forgive him for his transgressions and actions. Remember that forgiveness is for you, not for him. It allows you to move on without carrying all that pain around with you.
Married 6 together 8 Me:38 W:31 second marriage for both SS12, SD10, S6 Bomb: 9/8/11 (day before our 5 yr ann) W moved out: 2/18/12 D final: 11/12/12 Share S 50/50. Spend as much time as I can with SS & SD