At the end of the day, OP, you fundamentally don't trust your dp/dh. Whether this is because you're like my son's most recent ex, and simply don't trust anyone (I have no idea why she's like this) even though they're perfectly faithful, or because your dp/dh has actually played away/had an inappropriate relationship doesn't ultimately matter.
You don't trust him.
He may be innocent, and thoroughly fucked-off that you're still bitching about nothing two years down the line. (I would be.)
He may be guilty, have done nothing inappropriate since, and fucked-off that you're still bitching about it two years down the line. (Again, I would be; I made a mistake, lied about it, and feel uncomfortable that you keep raising the subject. I changed, ok, learned my lesson that you and our dc matter more, it won't happen again, now stfu.)
He may be shagging anyone who'll say "yes".
None of us, including you, can know the answer. Maybe Relate could help you, given dc are involved, or maybe your lack of trust means this relationship is over.
Only you can decide that.