The issue with the kids. Let him visit them at your place until you feel sure that he also has there best interest at heart and will do nothing further to confuse them. Which if they think mommie and daddie are still together but hmmm theres this other person with daddy to will confuse them.
Right now sounds like SO is having his cake and eatting it to. Because he is confussed. You might want to put him on a crash diet. Don't answer those late night calls. Let him call and talk to the children but if you have nothing important to tell him then let the calls end with the kids, And sex well I would say now is the time to go dark with that dynamic of the relationship now that you have confirmed that OW is still around.
Take him to a place where he has the option to miss you. To come seeking you.
