Is a husband considered a pimp (dayyūth) for forgiving his wife after her repentance from suspicious relationships, and is his action a disobedience to his parents, and is his brothers' act of exposing her correct, and what should the husband do regarding this situation?

If the wife repents and shows signs of uprightness, there is no harm for the husband in keeping her, as repentance erases what came before it. In this case, keeping the wife is preferable to divorcing her, and the husband is not a "dayyuth" (cuckold) by doing so. Rather, a dayyuth is one who condones wickedness within his family.

Her family should not incite him to divorce her after her repentance, for striving to separate a husband and wife is forbidden. Obedience to parents in divorcing her is not obligatory, and the husband is not considered disobedient by contradicting them, as long as the wife has repented.