TMB-
The halacha delegates each spouse specific obligations. The specific obligations I am talking about are the ones each spouse has the right to demand from the other in Beis Din, or force a get.
There is no specific halacha which states across the board that a wife is obligated to abide by the husband’s wishes. If what he wishes happens to be something in the ‘marriage contract’ so to speak, then she must abide by it, but not because his wishes carry weight per se, rather because this particular thing was agreed upon by them getting married. Therefore I don’t think the idea of one spouse having more authority in this area is accurate, because he/she never actually has authority, rather they are each bound by their own specific obligations to the marriage. I hope I am being clear.
My point is that you cannot show from the fact that a woman has many obligations in a certain area that this area is ‘the husbands domain’ or vice versa. Each spouse has requirements, and it ends at that. The rest should be decided through discussing and compromising.
Kasha-
It is said that a good woman does the will of her husband. It is not a halacha, but is considered proper. But I don’t think that is relevant, I think that refers to caring for him extra etc., not that she shouldn’t speak up if she disagrees with his mehalech, because she definitely has that right.