"Ultimately, I do want to be with my W because of our kid." That's a good enough reason, but its got to be on healthy terms too.
"Time to go back to the drawing board." Yes, quickly, and see a good lawyer on the way just in case the new design fails.
It's a good reason if you want to be a bad parent. She has cheated on him while being together with him and married to him while they have had their kid, it's safe to assume she'll repeat this past behavior again.
You would expose the kid to this?
You expect her to promise to be good and not engage in this behavior again?
