What should a husband do if his wife requests a khulʿ (divorce by mutual consent, initiated by the wife), and the court cites previous matters that occurred between them in bed, which they had agreed to cease, and he is now faced with two choices: admitting to them and destroying his family, or denying them before the judge?

If you have repented from forbidden acts, and your wife wants you to confess them before a judge to divorce her, she does not have the right to demand this. So, conceal your sins and do not confess. There is no harm to the wife in this that would necessitate divorce or khul'. If she is harmed by other matters, let her present them to the judge. As long as your wife is not justified in her claim, you are not obligated to confess. You may use allusive or ambiguous statements (ta‘rid and tawriyah) to free yourself from this injustice, similar to a situation where you are oppressed, and a ruler makes you swear an oath about something that, if you were to speak the truth, would lead to injustice or harm you.