Does a wife have the right to demand independent housing if the husband is financially capable, and his father is incapacitated, and the family refuses their departure from the house? And is it permissible for the husband to prevent his wife from visiting her family despite his ability to provide the travel expenses?

It is the wife's right to reside in an independent dwelling, and she is not obligated, according to Islamic law, to live with her husband's relatives. The husband must provide this dwelling for her according to his means. It is not permissible for the wife to travel to visit her family without her husband's permission. It is preferable for him to grant her permission, but if he does not, then she must be patient and communicate with her family through available means.