It is always recommended for the wife to obey her husband (as long as he is not asking her to sin of course) and she would be greatly rewarded for that. However, it is not mandatory for her to obey him in everything. She is to obey him in three things only:
1- Making herself physically available (unless she has a legitimate excuse like a medical excuse)
2- Not leaving the house without his permission
3- Not fasting mustahab without his permission
However, this applies if he is being reasonable. If he just wants to hurt her it doesn’t apply.
Let’s say he goes to work all day and he’s not home or he’s traveling, and he says to her you are not allowed to fast. Why? He just wants to annoy her. In that case she does not have to listen to him. Yes if he is home and he needs intimacy, then she’d need his permission to fast.