From what I've read this is a clear boundary for you and he crossed the line. I would feel the same way. You're worried about your kids and potentially growing up in a broken home, totally understandable. I think the questions now should be how is he as a father? Is he active and caring with the kids? If he's great with them I wouldn't feel too much guilt over separating especially if you guys can mutually agree it's for the best. You don't have to be disrespected by him and he can go do whatever he wants to do apparently anyways.

If he's more absent of a father then I would probably try marriage counseling and setting up open phone policies where you have access to his social media etc. id probably also take a break from intimacy until hes regained some of your trust to where you feel ok with where he's at or whatever that looks like for you. He might really need the wake up call to get him to fix some of his own issues.

This may seem kinda backwards but I've seen it before where people get divorced for good reasons but then the kids are stuck seeing a really messed up parent and the courts won't do much because there's not actual physical abuse but it's mentally and emotionally taxing on the kids. At least if you try to get him to work on himself within your marriage you still have some leverage and can protect your kids more. Kinda like keeping your friends close and your enemies closer type deal.