What is the ruling regarding a man saying to his wife in a moment of anger, "You are forbidden to me like my mother and my sister," and is this considered an oath of divorce or a Dhihar, knowing that he had intercourse with his wife afterward?

The phrase "You are to me as my mother" is not explicit in divorce or ẓihār. It is more appropriate to consider it an oath, as that is the least severe interpretation it can bear, which is the inclination of the Shafi'is; this is because the prohibition established by an oath is less severe than divorce and ẓihār. The expiation for an oath (kaffārat al-yamīn) is feeding ten needy persons, or clothing them, or freeing a slave; and whoever cannot find [the means to do so] should fast for three days. Anger is not taken into account unless it removes consciousness and awareness.