Does divorce take effect when an angry husband says to his wife: "Either you come to our house tonight, or each of us goes his own way," and what are the resulting Islamic legal rulings?

The majority of jurists hold that the divorce pronounced by an angry person is effective unless he loses his mind and does not comprehend what he is saying. The phrase: "Each one goes their own way" is a metaphorical expression of divorce, and divorce does not occur by it unless there is an intention for it. If the husband did not intend divorce by what he said, then his wife is not divorced.