Maybe you can explain to him that you need no contact to help get over what he's been doing. That you want to remain civil and be friendly for the kids. At this time though, you need space away from him to put yourself in a better place. That this space is just for yourself; just make sure that you emphasize that there is no OM. Just time for you. It's nothing personal against him; it's for you.
Also, let him know that what the kids are feeling is nothing that you control nor encourage. That's between your H and the kids. They will have to discuss amongst themselves.
I don't know if some might think this busts DB principles; but you have to comfortable with what you are doing. Just try to avoid any discussion about the M. There will be time for that when he quits seeing OW and wants to come home.
