Just as you are having to wonder how much he really loves you and if he will do this again and is just staying for the kids..
He also will have to wonder if you would have dumped HIS arse cold if you didn't have kids, and are just staying for the kids. Let him worry and vomit. He deserves that.
Except, my negative self speaking here, I've learned from reading that a lot of cheaters rarely think of things like that - that the BS feels more trapped and captive in a marriage after D-Day, being the one parent who does think about consequences for the kids before acting on impulse and feelings (dumping a WS), than a WS has EVER felt before the WS started his/her affairs for escape, impulse or those over-rated feeeeeliinggggs. The WS after D-Day seem mainly just to get pissed that their lives aren't perfect and their BS'es are unforgiving, unaffectionate and drama prone (crying, asking questions repeatedly). Then whining all the time that things aren't exactly happy for three to five years.
It's always bad news for a BS to hear that time is the only answer when the idea of feeling the agony for one more minute is devastating news. But as HeartacheAgain says, a year in a lifetime that you are waiting for the sake of your children isn't a wasted year in learning who you're really married to - a nice guy who made a mistake or a guy who feels entitled to have affairs when he wants. (Exception: Any spouse or kid being abused, and marriage should end that minute and the spouse walk out.)
Either way, you'll be having to deal with this guy the rest of your life until the kids are adults and then afterward at births of grandchildren and so forth. This year will let you know if you'd rather spend the next 18 years and plus dealing with him from a distance as an ex or in your home as your husband.