What is the ruling regarding a wife remaining without hijab while working with foreigners, knowing that she has the right to divorce?

A husband must oblige his wife to wear the hijab (definition), prevent her from mingling with non-mahram (definition) men, and ensure she does not leave the house except with his permission. This is based on the Prophet’s (peace be upon him) saying: “All of you are guardians and are responsible for your subjects. A man is a guardian over his family and is responsible for them.” And Allah, the Almighty, says: “Men are guardians over women.” If he approves of her immodest display (tabarruj) and mingling, it is considered cuckoldry (diyatha), and Allah has forbidden Paradise for the cuckold. If by "authority" you mean your statement, "your affair is in your hands," this is an authorization for her to divorce herself, but it does not remove the authority (over divorce) from your hand. If she allows you to be intimate with her after this statement, the authorization becomes void.