Welcome, sounds like it is an affair, and at least you need to deal with it the same way as an affair. Have you read Diveorce Remedy? You need to.
But to be an example to the kids, I think you need to focus on you. Take good care of yourself and try your bestest to not get pulled into H's affair, but this is sooooo hard!!! Stay busy, do things with the kids, and try not to pursue your H. Live your life as much as you can. You will be hurting inside but try to be as Happy as you can. Do it for the kids. Let them see a strong mommy. Good luck and welcome. You will get good advice here.