For what it's worth, my situation is somewhat the same. I admitted last month I was bi to my wife, and at that point the sex stopped. We're now seeking people elsewhere for romance, friendship or what not, but we have decided to live together to raise our son-we both want to be active presences in his life. I don't know how well this will work out. She's meeting up with guys, and so am I, since I've sat on these feelings for 30 years and now have the chance to explore the urges I stifled all this time.
Wife said initially she might be open to having sex from time to time, but that quickly went to a 'no way never again'. We sleep in the same bed though, a king size. We are trying so hard to keep our son secure in the idea that mommy and daddy will always be here for him (he's almost 8). My therapist, and hers, are not convinced we can make this work. We can't afford for me to move out and spend money on an apartment and other expenses; my wife doesn't work and thus any attempts to save for our son's college education or home expenses are lost on me living separately.
Point was this: how old are the kids? Are you ready to walk away from being a daily part of their life? Would your wife consider leaving them? It's one thing to try and repair a relationship, but if you feel it cannot be, for whatever reason(s), you have to decide if you can live with the aftermath, and what that will do to your kids. The kids are most important; they look to us for everything and I can't imagine the harm done if you aren't there for them.
I feel for you, I really do. I understand what goes through your mind. My advice: no sex. If it's done, don't treat what was once a loving gesture into meaningless physical action. It will only complicate things further.