The halacha is exactly as Kasha said. The man is in charge of the house and the wife is not allowed to say anything against him. She has to do the things the Rambam and the S”A say (washing him, serving him, ect). Besides this being halacha, it is pashut that it has to be this way.
Wolf if everyone is equal in a house then I think he needs to ask a shaila if he’s allowed to run the house that way. If not and a wife wont listen to a husband, he may be required to divorce her. She might be considered a moredes for not listening to him.