What should a husband do after discovering his wife's emotional and physical betrayal with another young man, and her conspiring with the young man's family to divorce him and marry him, especially given that the wife's family accuses him of oppressing her?

It is advisable to confront the wife with what has been discovered regarding her illicit relationship, and to demand that she repent and conduct herself with kindness. If she repents and shows remorse, then hold on to her and forgive her. However, if she does not show repentance, and it is highly probable that she persists in the sinful relationship, then separate from her through divorce (talaq) or khula', and conceal her affairs unless there is a benefit in informing her family, such as seeking their help in deterring her. If she asks for a divorce without a valid reason, or if she continues in illicit relationships and treats you poorly, then you have the right to refuse to divorce her and to put pressure on her until she forfeits her dower (mahr) or part of it, based on the sayings of Al-Sa'di and Ibn 'Uthaymeen.