I'll explain...your wife is having an EA and doesn't want to give it up. Your marriage likely won't make a great deal of headway until she truly gives him up...and that will happen in her own time. Even if she never contacts him again, she still may pine away and wonder whether she lost her soulmate.
I can't say that it sounds like you are giving her an attractive option to OM. I'd monitor her from time to time, but start getting out of spy mode. Maybe give her some space by getting out to do your own thing. Get busy with other things and do stuff with the kids.
It seems as though things are pretty frosty at the moment. You obviously can't push too hard, but you can still show some friendliness while also showing your independent side.
You cannot be lonely if you like the person you're alone with. Dr. Wayne Dyer