What is the ruling on a married brother living with his mother in the family home, which he shares with his sisters, and is denying him permission to live there considered severing ties of kinship or does it involve a legal doubt, especially given his mistreatment of his mother?

If the house belongs to the heirs, none of them may exclusively reside in it without the consent of the others. If all adult heirs consent to the brother residing there, whether as a donation, for rent, or on a rotational basis, there is no sin. If the heirs do not consent to the brother residing there, there is no legal transgression in that, nor is it considered a severing of kinship ties. The brother's ill-treatment of his mother is a major sin, and he must be advised, repent, and show kindness to his mother.