Addie,

Just ask him if he has contacted her lately. Don't accuse. If he says no then say that is good and walk away. You will then know that he is lying and where you stand. No confrontation about emails or snooping. Just knowledge. Confrontation will probably just cause anger and more secrecy. Im sorry but it looks like he is cake eating and you are the fall back plan right now. He should be trying to earn your trust not get back with OM.
If he lies then just keep on going with the move and stop the physical contact....