I think career and salary should determine who stays home.
Geez ! I worked so many hours that I rarely got to see them during the week. When my ex had to go out of town for a week once a month, then I was the Dad of the house as best I could. I would have liked to stay home with the kids but finances said NO !
I don't think so. They should work outside the home.
I think that if a parent is going to stay home it should be the one better suited to do so, Sometimes that is the father.