Wow, don't know how I missed this one... sorry no one has replied to you yet, mate, this is definitely quite an original scenario for here.
Opening up your relationship is a tough one, I have been there, sometimes it sounds great in theory and then when it actually happens it's quite tough.
Do you think it's possible to stay together as a family for the kids, but have your sexual needs satisfied outside of the marriage? Yeah, this isn't the 'conventional' way that realtionships are sold to us and how they're 'supposed' to work, but humans are sexual beings, and a lot of people - men and women- are able to successfully navigate having an open relationship.
You saying she doesn't want to leave, it sounds like she is happy with everything in the relationship besides the sexual part, and especially when you have kids, sex is such a small part of the whole package.
Do you think you'd be ok with staying together and having sex with others, or would it be too difficult for you to know she is doing that?