Is it obligatory for a wife, who is suffering from illness and fear, to move to an independent dwelling, if available, knowing that she cannot maintain her full hijab in the current shared dwelling with her husband's family?

A wife must obey her husband by moving to the residence he desires for her, unless there is a legitimate excuse, such as clear harm befalling her. The independent residence must be safe for the wife, and if it is part of the family home, it must have its own independent facilities. If the husband is unable to provide this, then the wife must be patient and fear Allah as much as she is able.