Thinking about it more...you should figure out what you want, what you can't deal with, and what you'd be able to live with, and ask your wife to do the same. It's important for kids to have consistent parental involvement, but that doesn't mean that the parents have to be married to each other- and if she doesn't want to be part of their daily life, then maybe it's better for her to just not have much contact with them than drift in and out of their lives based on whims.
Just try to think outside the box a bit. What if you got divorced, but shared a duplex so the kids saw both of you every day? What if you formed a MFM household? What if you continued a financial/parenting partnership, while each of you had other romantic/sexual involvements?
I'm wondering if her current attitude is how she really feels, or if she's just freaking out over the possibility of losing the new shiny. This is somewhat different circumstances (since she was cheating) but it's really hard having a relationship end (or even have to take a break) when you're in the middle of NRE and neither of you wants to end it---whoever or whatever comes between you ends up seeming like the bad guy, no matter how justified they were, or how hard you try not to resent them, because your brain is all jacked up on dopamine like a junkie, and they're stopping you from getting your fix. (Yes, I've BTDT, and I'm suspecting it'd be more intensely painful if all contact other than letter writing was forbidden, although it's probably easier to forget about someone if you aren't around them all the time....then again, it's probably easier to idealize someone if you don't have to listen to the snore and smell their farts and pick up their dirty socks that they leave randomly strewn around the house...) That's why some people refer to the retro-active veto as the nuclear option- it often damages or even destroys the relationship it was intended to save- even though in your case, it doesn't rationally apply because you hadn't given consent before things started, but junkies are not rational.