Is a man considered a Dayyuth if his wife works as a flight attendant, removing her hijab, mixing with men, traveling, and staying overnight outside the home, and her husband rejects this work but has not succeeded in convincing her to leave it, while he fears for his daughter from being negatively influenced by her mother?

It is not permissible for a man to let his wife work as a flight attendant, because he would be considered a dayyuth (pimp/cuckold), and a dayyuth is deprived of Paradise. If the wife insists on this work, then she is disobedient (nashiz) and loses her right to custody, because disobedience is an act of transgression (fisq), and a condition for the custodian is freedom from transgression. Custody then transfers to the maternal grandmother, and then to whoever follows in the order of precedence.