Is it permissible, Islamically, for the husband to be asked to sell a house gifted to him by his wife's aunt without any financial compensation, and to distribute its price among his brother and his cousin, knowing that the husband has no alternative housing or other money?

If your husband's maternal aunt sold him the house or gifted it to him without compensation, and he took possession of the gift and continued to dispose of it for a long time, then the house belongs to him and he has the right to dispose of it through sale or otherwise. He should ask people of knowledge about what is unclear to him, for Allah Almighty says: (So ask the people of the Reminder if you do not know).