What is the ruling on a husband saying to his wife: "Do not do this, and by Allah, if you do it – by Allah – you will not be my wife, and I will not know you," if the wife does this thing after his oath, or if she had done it in the past? And does this phrasing result in a divorce, and what is the expiation for the oath?

The husband's statement to his wife: "You are not my wife and I do not know you," is a kinayah (an ambiguous statement) that can imply divorce or something else. Therefore, divorce does not occur by it unless there is the intention [of divorce]. If the husband intended divorce with this phrase, contingent upon the wife performing a specific action, and she performed it, then divorce occurs. If he did not intend divorce, then it does not occur, and the reference point for this is his intention. If his intention was a threat, then he has the choice between fulfilling his threat or performing an expiation (kaffarah) for a broken oath, which is feeding or clothing ten needy persons, or fasting three days if he cannot find [the means]. If the action had already occurred in the past, then the husband does not break his oath by this threat.