Brian, you and your wife have good communication going for you, anyway. Think about that.
I agree that the children should come first. HOWEVER, that assumes that you staying together would present a happy facade for the children. If you get counseling and can turn that around, just enough, that might be the best solution.
However, given the reality of human nature, that is not necessarily going to be the outcome. Your wife wants a truly happy marriage partnership and you want your freedom. A good compromise would be living close to each other and sharing custody. The children still have a lot of access to both parents. They would still be missing the piece about an intact family, but on the other hand, they would be aware that a daddy living in the basement is not the model of a good marriage.
One of the over-riding factors in my divorce was that I did not want my sons to think that this is what marriage should look like.