All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is forbidden to cut ties with your mother because it is an obligation on you to obey and honor her as long as this obedience does not constitute any form of disobedience to Allah. Therefore, you are obliged to comply with the Commandants of Allah and His Messenger in this concern.
Allah Says (what means):
• {And We have enjoined upon man, to his parents, good treatment. His mother carried him with hardship and gave birth to him with hardship, …} [Quran 46:15]
• {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 honor. And lower unto them the wing of submission and humility through mercy, and say: “My Lord! Bestow on them Your Mercy as they did bring me up when I was small.”} [Quran 17:23-24]
In the same vein, Abu Hurayrah reported that once a man came to the Prophet and said: “Who is most deserving of my best companionship?” The Prophet replied: “Your mother”. “Who next?” the man asked. “Your mother”, replied the Prophet “Who next” he asked again, “Your mother” replied the Prophet . Then the man asked: “Who next?” “Your father” replied the Prophet .” [Al-Bukhari and Muslim]
There are other Quranic verses and Prophetic Ahadeeths that urge us to be kind with our parents, especially the mother. Know that severing ties with the mother is a major sin. So, fear Allah and know that your wife will not help you when Allah will hold you responsible for your deeds.
In addition, you have to advise your wife to be patient with your mother and to treat her kindly so that she can gain your mother's love and cordiality.
Allah Says (what means): {And not equal are the good deed and the bad. Repel [evil] by that [deed] which is better; and thereupon the one whom between you and him is enmity [will become] as though he was a devoted friend. But none is granted it except those who are patient, and none is granted it except one having a great portion [of good].} [Quran 41:34-35]
If the problem is solved, then this is what is required. Anyway, you should not obey your wife concerning separating yourself from your mother.
Know that some wives pretend in front of husbands to be wronged, while they are wrongdoers. They aim at driving husbands to mistreat their mothers or fathers. It is clear to you that such behavior is a way that leads to your destruction as Allah - linked the obedience to parents to worshipping Him Alone.
Allah Says (what means): {…and join none with Him in worship, and do good to parents, …} [Quran 4:36]
Also, the Prophet said: “Three kinds of people will not enter Paradise. They are: the one who is impious to one's parents, a procurer and a woman who imitates men.” [Al-Hakim]
It is reported that Allah delays (punishment) of all misdeeds according to His will until the Day of Judgment except ungratefulness to parents; He hastens punishment to one who is ungrateful to his parents before death. Parents' ill wish against a disobedient son may cause unhappiness to him both in this worldly life and in the Hereafter.”
Thus, it is your duty to obey and visit your mother very frequently whether or not your wife approves. If she applies for divorce, in word or deed, and she insists on it, then we say that the parents are more worthy of obedience and with greater reason.
In fact, it is not permissible for her to demand divorce, since the Prophet said: “Any woman who asks her husband for divorce without a genuine reason or harm against her, then it becomes forbidden for her to perceive the fragrance of Paradise.” [At-Tirmithi and Ibn Maajah]
Allah Knows best.