Does a divorce take place if the husband says to his wife: "If you don't like me, divorce me," and she responds with an acceptance, while the husband is unaware of the existence of the wife's delegated authority to divorce?

You delegated the divorce to your wife, but she did not choose to divorce, as evidenced by her statement "it will happen," and this is a promise that does not constitute a divorce. A promise of divorce does not take effect, nor is it obligatory to fulfill, nor is it recommended. Delegation has nullifiers, such as the separation of the spouses from the session of delegation, the husband having intercourse with his wife, and the husband retracting the delegation. We remind both of you to fulfill your duties towards each other, and divorce is not the only solution to marital problems.