I'm so sorry you're going through this. I went through this 6 years ago. My situation was different though in that we didn't have kids at the time and DH was hugely remorseful and worked his butt off to fix things. He arranged counseling and slowly over a couple of years built trust back. Now I can honestly say our marriage is better than it was before the affair. But it took a lot of work and if he hadn't been willing to put the work in I doubt I would have stayed.
It's a hard decision for you but I truly believe that if he has checked out and you stay, your resentment and unhappiness will just continue to build, and that will affect your own health and your kids. Only you know the answer. It listen to your gut.
wife of my soldier Steve, mama to my beautiful girls Rowan (11/07) and Linden (03/10)!