You sound a lot like my Dad. Based on that, let me tell you two things when he has expressed similar sentiments.
You know, men have that stereotype because most men like it and promote it.
And yes. Your experience as you described it is indicative of dominance hierarchy, just not in the way you're probably thinking. My daughter and I were actually talking about this the other day in regards to parental pressures and how nuclear families create an organizational system where there can't be any points of failure. Ever.
Your wife is having a hard go with her current pregnancy and you're having to pick up the slack. First off, consider how much less stress her illness would create if there were more family members and extended family to pitch in? Or better leave structure available? Or work flexibility? Right?
Now. Consider if you were a more typical kind of dude all notched up in your identity with the current extreme interpretation of Masculinity and in a situation where you need to support your wife while she's sick. Think about how that identity ideology might make you approach this time in your lives differently and how that might negatively impact you and your family and your family's future.
Because that's what's happening to a lotta lotta of people.
Maybe this article isn't for you. I can see how you might get defensive and feel attacked.
But. Take a good look around. A good hard critical look around. If you do like my Dad did, you're going to be disheartened at first to see how atypical you are. But then you'll be glad. Very very glad. Especially when the bodies start dropping around you and all these guys are dying miserable and alone. Especially when their kids won't talk to them and they've got nothing but their beer and their loneliness. You'll be very very glad.
Take care.
P.S. little girls love it when you braid their hair like parachute rigging. Every year for their birthday, buy them a tool and a toy.