There are some problems between his mother and his wife, and his mother wants him to live far away from her

Firstly: 

There is no doubt that the mother has the greatest rights of all people over her son, and that honouring her is one of the most important duties. Allah says (interpretation of the meaning):

“And your Lord has decreed that you worship none but Him. And that you be dutiful to your parents. If one of them or both of them attain old age in your life, say not to them a word of disrespect, nor shout at them but address them in terms of honour”

[al-Isra’ 17:23]. 

Allah has enjoined kind treatment of others too, whom the individual is enjoined to treat kindly, as Allah says (interpretation of the meaning): “Worship Allaah and join none with Him (in worship); and do good to parents, kinsfolk, orphans, Al-Masaakeen (the poor), the neighbour who is near of kin, the neighbour who is a stranger, the companion by your side, the wayfarer (you meet), and those (slaves) whom your right hands possess. Verily, Allaah does not like such as are proud and boastful”[al-Nisa’ 4:36] and the Prophet (blessings and peace of Allah be upon him) has enjoined giving everyone who has rights their due [See: Saheeh al-Bukhaari, 1968]. Hence the rights of the parents, especially the mother, take precedence over the rights of all people. 

It was narrated that Abu Hurayrah (may Allah be pleased with him) said: A man came to the Messenger of Allaah (blessings and peace of Allah be upon him) and said: Which of the people is most deserving of my good companionship? He said: “Your mother.” He said: Then who? He said: “Then your mother.” He said: Then who? He said: “Then your mother.” He said: Then who? He said: “Then your father.”

Narrated by al-Bukhaari (5971) and Muslim (2548). 

But this does not mean that a person should not give other people their rights; rather he has to give everyone who has rights his due, as stated above, and he has to strike a balance between these rights and fulfil his duties to the people around him as best he can and know how to run his home and his affairs well. 

Secondly: 

These problems between the wife and the mother are a common and ancient problem. The wise man who is guided is the one who looks at his situation positively and reduces problems as much as he can and closes the door to them. For this reason one of the rights that the wife has over her husband is that he should provide her with separate accommodation. 

It says in al-Mawsoo‘ah al-Fiqhiyyah (25/109): 

Putting the parents and the wife together in one home is not permissible (and the same applies to other relatives). Hence the wife has the right to refuse to live with either of them, because it is her right to have separate accommodation where she feels safe with regard to herself and her property. No one has the right to force her to do that. 

This is the view of the majority of Hanafi, Shaafa‘i and Hanbali fuqaha’. 

The Maalikis are of the view that a distinction should be made between the wife of noble birth and the wife of lowly birth, and they say that it is not permissible to make the wife of noble birth and the parents live together in the same house, but doing that is permissible with a wife of lowly birth, unless making the wife of lowly birth and the parents live together will cause her some harm. End quote. 

Undoubtedly the picture that you have painted of the relationship between your mother and your wife dictates that their living together in one house is not possible and that separating them is obligatory, especially since the mother is the one who has asked for that. So you must hasten to do that and it is not wise to think of the other solution, which is divorcing your wife. This is not a solution to the problem, especially if you have any children from her. Moreover the problem may arise again with any other wife whom you bring to live with your mother in the same house. 

So what you should do is hasten to do this as soon as you can, which is looking for a separate house for you and your wife. If you want to be close to your mother, so that you can be in constant touch with her and take care of her, then try to find your new house as close as possible to your mother's house, so that you can pop in to see her every time you come or go. In this way you can treat your mother kindly, relieve her of the burden of problems with your wife and keep in constant touch with her, whilst at the same time doing what you are obliged to do for your wife of treating her kindly and giving her accommodation that is suited for her. 

See the answer to question number 97810 . 

We ask Allah to guide you and set your affairs straight. 

And Allah knows best.