You've been betrayed and it hurts no matter how much leaving is your idea. I was in your place, worked on getting out of the marriage without causing hurt feelings (as much as that's possible) and trying to ease the kids into it. Within a couple of weeks after he finally left, I found out he'd been having an affair for nearly a year! I was pissed!
It won't take long for you to get past this and thank her for making it easier.
Some men just need another boat to jump on to when they see theirs sinking!