First of all you don't tell the children anythings as to why you separate, other than "Mommy, and Daddy are having problems getting along, and need a "time out" from each other.
This infidelity is between you and your husband, not the children. As much as this will effect them, he has not gone out on them, but on you!
You can read literally hundreds of post from women whose husbands only admitted the minimum of what they may have thought they were caught at, to later have to come more clean, only when caught more. (Women are just as guilty, but on here you don't see many of us men admitting these things , to our own detriment)
I don't know your husband, but I know your story, and have seen it on here time and time again. I would not believe anything coming out of his mouth, especially if he refuses to quit talking to the sleaze.
He has made a vow, and at this time it appears to have forgotten it, or cares less what a vow means. The thing you need to worry more about is what kind of example are you setting for your 3 and 5 year old, as far as what is acceptable behavior for a man to treat a woman, if one of your children is a male, and what is acceptable behavior for a woman to accept from a man, if one of your children is a female.
My heart goes out to you, and I hope this helps. Please keep us posted, as I am sure your situation will be valuable for others that come behind you. Good luck!