I suggest starting on a dual path: First, prepare yourself financially for the possibility of being on your own. See an attorney and see what you would be facing in terms of the financial dissolution of your marriage. This should help you prepare for what you need to do for yourself and your children, and it will help you to establish a time-line for when you actually walk out the door with a sense of security.
Second, when you're ready to throw down the gauntlet, tell him that you're aware of his infidelity, and that if he wants to continue with the marriage, he'll have to stop cheating and make a strong effort at couples' counseling. You have to be prepared for a variety of reactions, because he honestly may not value your relationship like he once did. This does not affect your value as a human being. If he doesn't want to continue with the marriage, thank him for his honesty and let nothing hold you back from taking some time to get to know your single self, and then finding someone for a mutally loving relationship.
Either way, therapy is probably necessary for both of you (staying together) or you yourself (if you're divorcing). I would think that it would be a good idea to annouce the divorce, if there will be one, to the kids as a couple, but a therapist can tell you for sure. Anger might seem like good company, but because of your kids, you have to be especially carefull about maintaining a sense of decorum if divorce is the road you choose.
On a lighter note, watching, "He's Just Not that Into You" and reading Steve Harvey's, "Act Like a Lady, but Think Like a Man", have a funny way of bringing home some need-to-hear truths regarding relationships and dating.
Good Luck to you. You have more power than you think you do! Use it wisely.