Try to see your H's contact for what it is, he is trying to stay connected to you. He doesn't want you to go too far.

If his A doesn't work out, he wants to make sure you are still around.

Don't make it easy for him. Make him doubt himself. Let him feel the fear of not knowing if he made the right decision to leave you. The only way to do that is to go no contact.

When he texts, he doesn't really want to know about the kids. He wants to know you will respond. He is in an A, that's all he cares about.

He uses the kids as his connection to you. Pull way back. Make him sweat.

YOU are a beautiful, loving, caring, kind person. Know your worth.