Sounds like the family meeting went well, all considering. How do the children feel right now? What was their reaction?
Adding on to LH’s post, I think the hardest thing for you right now is going to be sitting back and letting him fix this mess on his own. Making his own IC and Drs appts, not asking him about it all, letting him repair his relationships with the kids (and you not getting in between their anger towards him), and most importantly, not reminding him of his commitments to doing XYZ (not verbally, anyway, but keep up your boundaries). Let HIM be the one to come up with a transparency plan, including tracking if that’s what he wants to include. (You of course can decide if it works for you or not, but he needs to take the next steps) The more he does this on his own, the better the outcome for you as a family. He broke it, he fixes it. Don’t step in. The only person you can save is YOU.
You have the right mindset, letting his actions speak louder than words. Stay strong, be brave and remember how mighty you are!