The question you asked is do you let him in now, later or not at all.
I think the question I have to ask, is do you want to let him in now, later or not at all?
I am assuming that the OW was the reason you are split up, and that the OW is no longer in the picture. Are you assuming that he is going to find another one down the line?
My bias is to let him back in. One because he obviously cares for you and wants to be with you. Secondly, it will probably be better for the kids. And finally, because you seem to care for him too, and would be happier with him in the house with you.
Obviously, you need to come up with guidelines, and some very specific consequences for cheating that you feel you are willing to stick with. You probably should even come up with something that addresses any kind of internet cheating that is becoming such a fad these days.
But basically, you have to look into your own heart and decide what to do.
divorced in 2003 Married in 12/2005 born 1948 wife born 1958 divorced in 2001