What is the ruling on someone who said to his wife, "(O illegitimate daughter)"? Can she ask for implementing the prescribed corporal punishment on him or not?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If the husband or anyone else says to his wife or whosoever: "O illegitimate daughter," then this is considered a slander to her parents. What is meant by slander is an accusation of adultery, whether explicit or implied.

Slander is prohibited and is one of the seven destructive sins that doom a person to Hell. Abu Hurayrah narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: “Avoid the seven destructive sins.” As he counted them, he said: “…and slandering chaste, unaware believing women.” [Al-Bukhari, Muslim, Abu Daawood and others]

Also, Allaah Almighty threatened those who slander others with curse and severe punishment. Allaah Almighty says (what means): {Indeed, those who [falsely] accuse chaste, unaware and believing women are cursed in this world and the Hereafter; and they will have a great punishment. On a Day when their tongues, their hands and their feet will bear witness against them as to what they used to do.} [Quran 24: 23-24]

Whoever slanders others and does not support his accusation by the testimony of four witnesses who have seen the penis enter the vagina as the (kohl) stick enters into the kohl jar, then the case is referred to the judge and he must be given eighty lashes as a prescribed corporal punishment. Allaah Almighty says (what means): {And those who accuse chaste women and then do not produce four witnesses—lash them with eighty lashes and do not accept from them testimony ever after. And those are the defiantly disobedient.} [Quran 24: 4]

Accordingly, the one who accuses the parents of his wife of adultery has to repent to his Lord and never do that again. Allaah Almighty says (what means) regarding those who repent of slandering people: {Except for those who repent thereafter and reform, for indeed, Allaah is Forgiving and Merciful.} [Quran 24: 5]

 Allaah Knows best.