My boyfriend is emailing his ex-girlfriend - what should I do?

Before making any decisions i would look into the situation a little more. I find it hard to believe that they had a nasty break-up and are now asking how each others day went. Checking in on kids is one thing and should be a once in a while thing, but it sounds like they are talking frequently. It might just be a ploy to get his foot back in the door with her, then again it might be innocent. I would just monitor the situation. You have asked him twice to stop, and now it is time to sit back and see if he continues. If he stops you I think you have nothing to worry about. If it continues It might be time for an ultimatum. Simply tell him to stop or you are going to start to see other people. At that point if he continues to talk with her, you just need to get rid of him. Whatever you do, just be cool. Don't over react, even if you have to give him the ultimatum. Be Cool.