What is the religious ruling regarding a husband who had intercourse with his wife after divorcing her with a revocable divorce, without informing her, and then divorced her a third time?

Your brother's statement to his wife, "She is now divorced," constitutes an effective divorce by explicit utterance. If this was the second divorce, then his subsequent statement, "I have no desire for her," is an ambiguous divorce pronouncement (kinayah). If he intended by it to initiate a divorce, she becomes unlawful for him until she marries another husband. His cohabitation with her then becomes forbidden. His divorce conditional on her leaving is void because it does not correspond to a valid object. However, if he did not intend a divorce with his previous words and he reconciled with his wife before the completion of her waiting period (iddah), his reconciliation is valid.

As for his swearing by divorce if she left, and then he broke his oath, it is considered a third divorce if it was preceded by two divorces. In this case, she becomes unlawful for him according to the majority of scholars. However, according to Sheikh Al-Islam Ibn Taymiyyah, he is obligated to pay an expiation for an oath (kaffarat yamin) if he did not intend a divorce. Informing the wife is not a condition for the divorce to take effect. As for the man's guardians, their role in this matter is limited to enjoining good and forbidding evil.