Deb - Quit waiting for him to email. Email him yourself - often!!!!! Clearly he responds to the attention. Don't leave a void for OW to fill. Send him silly things, brief notes that don't require a response, jokes, pictures of you(so long as they are appropriate for the work computer). I'm guessing he'll have a harder time gettting sucked into her drama if every email from her is followed by a cute, funny one from you!
Ellie PS - Do the kids HAVE to move in with you? I'm getting a bad feeling about this. Can you ask H if there is some other way he would like to handle it? Could you loan them money for rent somewhere else? Just feels like right now is a very bad time to have that additiona;l stress at home. I know it's tough to come up with the money, but still cheaper than divorce!