How often do you drink so heavily that you can't go visit your kids as planned?
I'm going to be blunt: this (DBing, esp. when there is infidelit involved) is the single toughest thing you will have likely had to do in your life, and you're in for a long, tough battle REGARDLESS of which path you take. And the battle will take 12-24 months, on average.
You need to summon ALL of your wits about you, to protect yourself and your kids, and give yourself the best chance of restoring your marriage, if that's what you decide to do. Getting drunk before dinner on a workday, and disappointing your kids, is NOT very attractive to your wife, and NOT the condition you need to be in to face this storm.
Make no mistake -- THE STORM IS HERE. You can push thru it, or you can let it consume you.