What is the religious ruling on the wife who went out without a head covering (hijab), with her husband conditioning her divorce upon this act? And is this considered a conditional divorce?

This is a conditional divorce (ta'liq al-talaq (definition)) of the wife, contingent on her going out without a hijab (definition). If that occurs, the divorce takes place. The husband's lack of knowledge does not prevent the divorce from occurring. If this was the first or second divorce, the husband may take his wife back without a new contract, and the return (raj'ah) occurs through sexual intercourse. The spouses are advised to avoid anything that leads to discord and to resolve problems with wisdom, far from divorce.