Is it permissible to describe a man as a "dayyuth" if he allows his wife to work in public institutions or mixed schools where women and men converse together, and his wife goes out displaying her adornments, while he is aware of the presence of this mixing?

A jealous man does not permit his wife to go out adorned and mix with men, because it involves dayouthah (pimping/cuckoldry), which is the opposite of the gheerah (protective jealousy) enjoined by the Sharee’ah. Gheerah is one of the qualities of the believer and the traits of manliness. Allah’s Gheerah is for His servant to commit that which He has forbidden. A man protects his wife from being seen by non-mahram men; he is her maintainer, obligating her to fulfill the rights of Allah and restraining her from corruption. He is a shepherd over his family and responsible for his flock. If someone is lenient in this regard, he must be advised and reminded of his responsibility before Allah.