Is it permissible to force one's wife to wear the hijab, or else divorce her, out of fear of people's perception, and does this action contradict the principle of "there shall be no compulsion in religion"?

If lack of hijab (definition) means uncovering the head, then you must obligate your wife to cover it after attempting to persuade her kindly. If she does not respond, then consider divorcing her for what is most beneficial, bearing in mind that the presence of a Muslim woman in a non-Muslim society does not exempt her from wearing the hijab.

If what is meant by hijab is covering the face, then the matter is less strict, and there is no harm in uncovering the face and hands when there is a need or necessity.

As for your statement to your wife, "Otherwise, I will divorce you," it is a promise of divorce and does not constitute a divorce.