What is the ruling on a woman working in a restaurant where there is gender mixing, given that her father is present as a supervisor?

It is permissible, in Islamic law, to open a restaurant. The employment of workers of both sexes within it is also permissible, provided that it does not lead to 'fitna' (temptation or discord), such as impermissible seclusion (khalwa (definition)), unlawful mixing (ikhtilat), or immodest display (tabarruj) and unveiling (sufoor). If it does lead to 'fitna', then it becomes forbidden. A woman's staying in her home is preferable, but she may go out to work when there is a need, provided Islamic guidelines are observed.