He cheated and betrayed you sexually, financially, and flat out lied to you. I have been through divorce (as a child and as an adult), and trust me, the kids make out fine. In fact, my kids love it more because now Santa visits them twice. :-)
Here's the bottom line... If you can't trust him then it isn't a life worth spending looking over your shoulder. Wondering if he is doing it again, watching every transaction in the bank account, and you will.. Your kids may not understand today (depending on age of course), but they WILL understand later as they get older and have relationships of their own..
As Dan says, this isn't a simple matter of "cheating" this guy is an ass who stole and betrayed from his own family just for a piece of ass on the side... MEGA PARTY FOUL...