If the house is owned by the wife, does the husband no longer have authority over her, and is he not entitled to command her so that she obeys him? Is it permissible for the wife's family to stipulate that he not hit her? And what should be done if she becomes disobedient (nashazat)?

The husband's guardianship over his wife is firmly established and is not affected by the ownership of the house. She must obey him in what he commands, as is necessary. It is not permissible for the wife or her family to stipulate that the husband should not administer a lawful disciplining blow to her face, and he is not obligated to fulfill this condition. If she shows disobedience (nushooz), he has the right to discipline her as Allah Almighty commanded. It is worth noting that refraining from striking is more preferable, even if it is permissible.