My thoughts are that it depends on the relationship with the ex. If there are children involved, then it's pretty much necessary...but from your post it doesn't sound that way to me.
I don't think I'd care to share a relationship with an ex. I don't think I'd care to live with anyone who lied to me about these things, even if they 'fessed up later without a solid plan to assure me it would never happen again. And I don't think I'd want to spend my life wondering what he was up to.
But that's just me.
I'm sending hugs and prayers because I know this isn't easy for you. It's easy for me to say because I'm not in that situation, but in the end only YOU can decide what's right for you.
Hugs