I agree that you need to validate your kids feelings, and not tell them they have to put up with W. Trying to put yourself in between as a buffer is just going to end badly. Especially the grown up ones. But do not undercut the relationship, either. That is important.
I also agree that maybe public school would be a decent choice for the littler ones. Esp. if your wife is looking at moving out.
Me: Mid 40s W : Early 40s M:11 T:13 S, D, both 7-10 BD : 11/2017 Separation : 1/18