The husband's father and mother have no authority over their son’s wife
Question

Who has the right to be obeyed: the husband or his mother? What if the mother gives some instructions and the husband gives different instructions -- who is to be obeyed? Especially if the husband and his wife are living in his father's house? 
What if the parents tell their son to tell his wife that she should do something, and the husband objects to that? Is she in turn obliged to listen to what her in-laws tell her, against the objections of her husband?.
Praise be to Allah.Many shar‘i texts indicate that a woman’s obedience to her husband takes precedence over her obedience to any other person, even her own parents, so how about people other than them? 
Shaykh al-Islam Ibn Taymiyah said: When a woman gets married, her husband has more authority over her and her parents, and obedience to her husband is more obligatory for her. 
And he said: She does not have the right to go out of his house except with his permission, whether her father or her mother or someone tells her to do that, according to the consensus of the imams. End quote. Majmoo‘ al-Fatawa, 32/361 
So the husband's father and mother do not have any authority over the wife and she is not obliged to obey them in what they tell her to do, whether the husband approves of that or not. The most that can be said concerning this matter is that she should respond to the wishes of her husband's father and mother as much as is required to be kind and maintain a good relationship, within the scope of her ability, but only in that which will not conflict with obedience to her husband. 
The scholars of the Standing Committee said: There is nothing in Islam to indicate that the wife is obliged to help the husband's mother, except within the bounds of kind treatment and as much as she is able, out of kindness towards her husband and out of respect to her duties towards her husband.
Fatawa al-Lajnah al-Daimah, 19/264, 265 
In that case, the role of the wise and smart husband is to help his wife to avoid conflict with his family or confrontations with them; he should take matters into his own hands from the outset and try to be kind when reconciling between them and prevent division between them. 
If it is possible to have separate accommodation for himself and his wife, that is what he must do and that is better in order to maintain good relationships and keep his life free of headaches. 
Please see also the answer to question number 6388. 
And Allah knows best.