I wouldn't cover for him with the kids. Kids aren't dumb and they're going to know eventually ... if he won't tell them about OW I understand you not wanting to push too much on them but don't let him act like this was a joint decision ...make sure they know this was dads decision.
When he asks to talk next time just say H you've chose to leave and your with OW. Short of the kids or bills there's nothing to discuss. If it's legal have your L contact mine. Bye!
You don't neee to keep saying the same thing we don't need to talk over and over because he will see through it.