Sounds like your wife got all of motherhood and half of fatherhood
I experienced the same thing. When I was alone and in charge, everyone got fed, bathed, bandaged, etc. Everyone survived despite the fact that mom was at work. When she was home, I didn't do things "right".
What I discovered over the years (kids are now 15, 13, and 11) is that if you are patient, the children will make your argument for you. Eventually, if she isn't completely delusional, she will realize she doesn't know any more than anyone else. At that point she will welcome the opportunity to share the decision making as well as the blame.
Of course, it probably helps in my situation that we usually agree, and love each other, and our mutual goal is to get the kids raised well enough that they can get jobs and move out of the house.