Is it permissible for a woman to request a home independent of her husband's family, knowing the circumstances of the husband's mother and that the husband works one month and is off one month?

The minimum that a husband must provide for his wife in terms of housing is a decent, independent room with its facilities (door, kitchen, bathroom). It is not a condition for it to be completely separate from his parents' house; rather, it is permissible for it to be a room within a house where his family resides. The dwelling must be suitable for the husband's financial situation and independent for the wife, unless she herself chooses to share with his family. In the case of the husband being absent for a month and present for a month, it might be most suitable for the wife to stay at home with the husband's mother, exercising patience with any inconvenience that may arise.