Does a divorce pronounced by a man in a state of extreme, uncontrollable rage, yet fully aware of his words, become effective, given that his wife's actions provoked him to it?

The default ruling is that a divorce pronounced by an angry person is valid, unless their anger reaches a point where they do not comprehend what they are saying, based on the Prophet's (peace be upon him) saying: "There is no divorce in a state of 'ighlaq' (extreme anger/compulsion)."

If the husband comprehended what he was saying when the divorce occurred, he may reconcile with his wife with a new contract and dowry if the 'iddah (waiting period) has ended, or without a contract and dowry as long as the 'iddah is still ongoing, provided it was the first or second divorce.

It is necessary to beware of anger, as it is an entry point for Satan to corrupt the marital relationship.

The wife's act of hitting and assaulting her husband is a serious matter, involving abuse, disobedience, and sin against Allah, which necessitates repentance and apologizing to the husband, unless it happened involuntarily due to anger, in which case there is no sin upon her.