Is a husband's saying to his wife about her father: "The origin of your father is that his mother committed adultery with him" considered a slander (qadhf) that necessitates the legal punishment for slander (hadd al-qadhf), and what must be done to implement this punishment, knowing that the speaker is aware of the father's and his mother's honor, and intended by his words to provoke his wife?

Slander and insult are forbidden. Your statement about your mother-in-law is clear slander, and it is one of the gravest sins, necessitating the prescribed punishment (hadd) if the slandered person or their guardian demands it. If they do not demand it, the hadd is not carried out. You must repent sincerely by abandoning the sin, regretting it, and resolving not to return to it. You should seek forgiveness from the aggrieved party if they are aware of the slander; otherwise, refute yourself in front of your wife.