Is it permissible to reconcile with the wife after two divorces occurred in anger and two other divorces occurred in front of her family, knowing that the waiting period (iddah) has not ended? And can this be done without her family's knowledge, or does it require going to a ma'dhun (authorized marriage official)?

If anger deprives a person of their awareness, then the divorce does not occur; otherwise, it does.

The number of divorces depends on the speaker's intention. If he repeated the word "divorce" twice and intended two divorces, then two occur. If he intended emphasis, then only one occurs. However, if he said, "You are divorced, you are divorced," then two divorces occur. But if he said, "You are divorced, divorced," then only one occurs.

If two divorces occur for the first time, the wife becomes irrevocably divorced (baynunah kubra) and is not lawful for him until she marries another man. However, if one revocable divorce occurs, he may take her back before her waiting period (iddah) ends, without needing her consent.

It is advisable to present the matter to trusted local scholars.