Zahra submits to Zaton in the bedroom, but outside of that, they are very much a unit and rule the House as a couple presenting an united front, and have done so for 20 +years.
She is a strong woman and every other member of the House is subservient to her.
Especially when it comes to disciplining Ain, she has at least as much if not more of a say in the matter as the MC.
They had agreed that Ain needed to be punished to understand the severity of what she'd done. For the MC to start thinking with his dick halfway through and turn the punishment into a kinky pleasurable moment both for him but, most importantly, for Ain, was, out of game, fan service.. in game it was actually a mistake on his part, devaluing the lesson she was meant to learn, and she rightly so points this out to him. He has a soft spot for his daughters... She knows better. Ain needs to learn.
In the end though, he still got to shoot his load, if you so decided.
The MC does not give her a hard time over her criticism/speaking up about it, precisely because he knows she's right.
As much as he knows he is and acts as the head of the house in front of everybody, privately he values and respects his wife's opinions and voice and takes no pleasure in disappointing her, especially when she's right. Also, she's got a mean/fearsome streak of her own, as you will have seen with the Fairy scene.
Ultimately they are marriage goals, and she's not just a pretty body for him to enjoy, irrespective of what the common notions might be about how harems should be structured in these games. Their dynamics are more complex, or at least that's what we're aiming to portray.