The only “authority” a husband can exercise is that which his wife consciously gives him. Society’s depiction of the man ruling over the home with a fist is an utter fiction (and a vile lie, from the feminists).
In practice, she holds all the “power” in the home.
She can resist any decision simply by talking, crying, fulminating, and talking, and talking…, until he gives in.
I point to my case, where my wife knew well that my number one goal in life was the religious formation of our children, and which she couldn’t care less about. Thus she could get away with anything by parceling out my involvement with the kids.
YMMV, but SAHMs don’t have a lot of control over our lives. We have to accept whatever the terms of our husband’s employment is and work around it. If our husband gets a job two or three states away, we’re moving, and his job has take priority over everything else. If there’s not enough money, we have to make it work (if we’re doing our job, of course). If he says he’s busy working, then we don’t get help with the house or kids, even when we need it. If he’s bad with money, we can’t stop him.
When my husband and I were having a hard time, I literally could not leave the house by myself unless I got him to agree to take Baby Girl. It was like being in jail, but at the time, I wasn’t able to express to him how unfair it was that he could come and go at will like a free adult, but I was dependent on getting his permission to go anywhere by myself.
Also, my husband would grill me over tiny expenses, even though he makes a great income and I had been a very careful money manager. This all felt really degrading and humiliating. The stuff he did at the time (like quizzing me on whether I really needed to go to the grocery store even when I was taking Baby Girl–he thought I should only go once a week) really hurt my self-confidence at a time when I felt overwhelmed and lonely and was probably teetering on the edge of depression. If I’m not smart enough to decide when to go to the grocery store, what am I smart enough for?
Like it or not, this felt a lot like the “iron fist” that you think is mythological.
My husband has (thank goodness!) stopped doing this stuff when he realized how terrible it was, and the worst period was less than half a year, but it was that bad.
Lord knows what would have happened to my mental health, had I been a “submissive” wife in the sense that omgriley and Vonsalza use the word.
Edited to add: This low point was what caused me to start reexamining my old ideas about wifely submission and start thinking about whether those ideas actually made sense. I also realized that my bad ideas about wifely submission were part of what got me to that low point. You cannot imagine how surprised I was to find the quotes in Casti Connubii I’ve been talking about and realized that up until that point, I’d been carrying around essentially conservative Protestant notions of the wifely role. As a new convert, it never occurred to me that the Catholic theology might be rather different.