Can't you take charge and tell the kids yourself that you're getting divorced? I know you've said you're an avoider and that will be hard but your H won't tell them because he isn't interested in divorce. He wants you and that piece of junk he's involved with.
You will do whatever you're going to do but I think pitch darkness i.e. uttermost blackness is in order, like Dr. Harley's Plan B. Lovingly tell him there will be no contact of any kind at all until/unless his antics end, then back it up.
Take the legal measures to get it all done, have all of his stuff moved, set up an intermediary for all communication relating to the kids, change phone numbers and email addresses then go dark and silent. Uttermost darkness.
His secret, 2nd life in the other city made this diaster possible. If there's hope for you this would need to stop, permanently.
My heart really does go out to you.
GH31
Me: 46 W: 46 T: 23 M: 20 DS12 DD11 DS5
W left: 01/28/08 Discovered OM: 02/26/08 W back for 9 days: 04/08 W returned 05/21/08 EA/PA - 01/08-07/09 W's MLC 2008-2014 (realised this much later)