Dude I did just that. It's in a couple of posts back. I told XW it is inappropriate but she is defensive and gave some excuse she didn't teach them. She didn't see it as a problem and said because he's always around that kids he's like a daddy.
I even tried to set up a meeting with OM but he did not turn up. Texted him my 'thoughts'.
It seems to me that you approached W a bit too tentatively when saying it was "inappropriate" that your kids calls the OM 'Daddy.' You need to man up and really confront her about that. Show 'em who's the real Daddy here!!!
Don't bother acknowledging the OM at all. No emails, no texting, no talking about him. He is nothing. The OM is not a part of your marriage. Remember that.