He is not even close to seeing the power lies within to stop the cycling. I believe you'll know he's there when he seeks non-court ordered psychiatric help. He has a lot of issues, and he knows that, but as long as he runs from them, it won't get better.
The marriage hurts.
Give yourself time and space to grieve. It punched me in the gut harder than I expected, but I'm okay now.
But be mindful of some things regarding the union, too. If it's not legal - how does this impact his probation? Because bigamy is a crime, and committing a crime while on probation may nullify the probation, correct? Does his probation officer know what's going on?
If it IS legal - transfer as many joint assets as possible right now into your name. Bank account will become half hers. House will become half hers. That's a lot of why these women do it. If you can get a text or email where he declares it to be yours - all the better, but not as legal as legally making it all yours. This is to protect what you've shared, and most importantly - the kids.
Have a backup plan if she suddenly starts pushing for visitation with the kids out there. Not to be scary, but we know from other threads here that sometimes they just do it to be mean to us, because they CAN. Go into mama bear mode.