At my wit's end

[MrBond]

It's perfectly easy to "kick him to the curb" even with kids.

Let's put it this way. You don't know if he's going or when he's going to leave. You and your kids have no stability. Do something different.

Establish the boundaries. Be sure he "breaks up" with the OW with you in the room and he has to have absolute transparency.

Have you two been to counseling before? He has to have the addiction to the OW broken.