Praise be to Allah.
This wife is not obliged to obey her mother in what she is telling her to do, or to agree to that, for two reasons:
The first reason:
There is no obedience to any created being if it involves disobedience to the Creator, whether the one who is issuing these instructions is a parent, a ruler or anyone else, because of the general meaning of the words of the Prophet (blessings and peace of Allah be upon him): “There is no obedience if it involves disobedience [to Allah]; rather obedience is only in that which is right and proper.” Narrated by al-Bukhaari (7257) and Muslim (1840). And he said: “There is no obedience to any created being if it involves disobedience towards Allah, may He be glorified and exalted.” Narrated by Ahmad (1098).
For more information, please see answers no. 11872 , 1176 and 119411 .
The second reason:
It is not permissible for the wife to seek divorce when there is no legitimate shar‘i reason for that. There is a stern warning addressed to the one who seeks divorce when there is no problem. Abu Dawood (2226), at-Tirmidhi (1187) and Ibn Maajah (2055) narrated that Thawbaan (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Any woman who asks her husband for a divorce when there is no problem, the fragrance of Paradise will be forbidden to her.” Classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Because of what is mentioned above – as well as other shar‘i considerations – it is not permissible for this wife to give in to her mother’s demands. If visiting her mother or keeping in touch with her will help her mother to continue with these demands, or there is the fear that visits and other contact may lead to the mother influencing her daughter, then the wife may refuse to visit her on her own, and she may visit her with her husband or with someone whom the mother respects and will not be able to make that demand of her daughter in front of that person. She can also leave longer intervals between visits, as much as will alleviate her mother’s harm and negative impact on the daughter. Then she can try to find other ways to keep in touch and to honour her mother in a way that will not be harmful to her.
There is a stern warning regarding the one who tries to turn a woman against her husband. It was narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “He is not one of us who turns a woman against her husband, or a slave against his master.” Narrated by Abu Dawood (1860) and others; classed as saheeh by al-Albaani.
For more information, please see the answer to question no. 47040 .
And Allah knows best.