Is it permissible, Islamically, for a wife to refuse her mother-in-law's stay in her home if her presence causes harm to the household and its stability, and is this refusal considered impelling the husband to sever ties with his kin and be undutiful to his mother?

Legally, the wife has the right to have a separate dwelling where she is not harmed. Therefore, she has the right to refuse her husband's mother living with her in her private home if it causes her harm. However, the wife does not have the right to prevent her husband from bringing his mother to live near him out of filial piety towards her.

It is better and more complete for the wife to help her husband in his filial piety towards his mother and accept her living with them, out of patience and seeking Allah's pleasure, and then to please her husband; for her is a great reward.

The husband must balance his wife's right to private accommodation with his filial piety towards his mother. If his mother has no shelter or companion other than him, he may bring her to live in a separate part of the house with independent facilities, without interfering in the wife's affairs. He should also arrange for someone to serve his mother, as serving the husband's mother is not the wife's duty.

So, the wife should help her husband in his filial piety towards his mother, and demand her rights without that leading him to fall short in his duty towards his mother.