His wife does not want to fast

Praise be to Allah.

What your brother should do is strive his utmost to guide his wife to the path of truth. He should use all methods of exhortation and warning, reminding her of Allah and His rights, and pointing out the danger of what she is doing. Then he should strive to find her good friends, even if they are from among his relatives, such as putting her in touch with righteous wives of his friends, who can bring her useful tapes and pamphlets. If she obeys him, this is what he wants, otherwise there is no reason why he should not use such methods as forsaking her, if that will be useful in this situation. If forsaking is prescribed with regard to the husband’s rights, perhaps it is even more appropriate with regard to the rights of Allaah. 

It is narrated that Abu Umaamah al-Baahili said: I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say: “Whilst I was sleeping, two men came to me and took hold of my upper arm, and brought me to a rugged mountain. They said: ‘Climb up.’ I said: ‘I cannot do it.’ They said: ‘We will make it easy for you.’ So I climbed up until I was at the top of the mountain. There I heard loud voices. I said: ‘What are these voices?’ They said: ‘This is the screaming of the people of Hell.’ Then I was taken and I saw people suspended by their ankles, with the corners of their mouths torn and pouring with blood. I said: ‘Who are these?’ They said: ‘These are the people who broke their fast before it was time to do so.’” 

Narrated by al-Bayhaqi, no. 7796; classed as saheeh by al-Albaani. 

If this is the punishment for the one who breaks his fast before it is time, then what about the one who does not fast at all? 

If, in addition to not fasting, your wife does not pray at all, then she is beyond the pale of Islam, according to the correct scholarly view. Based on that, it is not permissible for your brother to remain married to her. And Allaah knows best. 

See also question no. 12828.