cheating husband, devastated stepdaughter

Your daughter will handle this as well as you do . . .

Perhaps letting this man be a human would be a first step. It was unreasonable to expect anyone would be "perfect" to her for her entire life.

He screwed up and wants to make amends. Until you let him regain your trust and put the marriage back together, she will not allow herself to let him earn his trust back either.

So, be a good role model for whatever you want to do. But let her know that he is a human, and that you are going to allow him to be just that.

He has amends to make, for sure.

First of all understand that it’s okay to be hurt, and to be angry. Both are very human emotions, and very understandable.
He does have some good qualities I see. I’m glad to see he wants to try with you still. Did he tell you what contributed to him straying? If you don’t understand why he strayed, you will find it very hard to ever trust him again. Understand that affairs depend on two things : The make up (ie emotional needs) of the person engaging in the affair, and the make-up (ie the exchanged meeting of each others needs) of the relationship. It may be that he will be a philandering fool no matter who he is with, or it may be that he was not having his emotional (by the way, emotional is very closely tied to physical, but not entirely dependant on the physical) needs met. You need to work out which it is.
You need to decide whether you’re truly going to give him another chance, which does not involve forgetting (that’s mentally impossible), but does involve actually giving him another chance.

And have you asked yourself ‘what do I want from my relationship right now, and in the future’ and ‘what is the best way to build towards that’?

Unfortunately this isn’t just about him earning your trust back – it’s about both of you (ie. you as well) putting in an effort to rebuild the relationship.

That doesn’t mean you have to throw yourself at him, because he does need to understand how much you hurt him, and he does need to earn your trust back. But you do need to look at your reward system to ensure you aren’t sabotaging his every attempt to rebuild trust.

Your daughters trust of him is not your issue. You have a bigger issue right now - your marriage. Your daughters emotional issues may tug at your heartstrings, but in the end, it is for her to come to an accomodation with her feelings, and if you are split between your daughters issues and your marriages issues - you may end up tying them together which may result in both being impossible to mend. I'd say worry about your marriage for first.

Also, as mentioned in a previous post – how you handle this will watched closely by her. She may eventually try to help, or she may even try to sabotage any headway you and your husband make - that depends on her (and is a major reason why you should not tie the two together)

Growing up, I watched my parents go through years of fighting. Their fights never made any sense to me. And they always blamed each other for what in the end, was silly nonsense. It was only after they divorced that I realised they had each wanted to separate for quite some time before they actually did, and the fighting was just their way of building up towards feeling justified (within themselves) in divorcing the other. Just make sure you aren’t staying in this relationship for the same reason.

If you haven't been forthright with him, and told him how much what he did hurt, then be forthright with him (but don’t be vindictive). Talk about your hopes, talk about your emotional needs, talk about who you are, and how when those things were broken how hurt your became. Let him understand who you are.

Best of Luck