What is the ruling on me saying to my wife in a state of intense anger, "If you go to school, everything between us is over," after asking her to quit her job, then retracting my decision? And is this considered a divorce or an oath and expiation? And what is the expiation?

What occurred is a suspended divorce using an indirect expression. According to the majority of jurists, it takes effect if the husband intended it and the condition upon which it was suspended is fulfilled. Some jurists are of the opinion that if he intended only to threaten and prevent, then it does not take effect. If he did not intend divorce, then the expression has no effect. The default assumption in case of doubt about the intention is non-existence [of divorce], in addition to the fact that indirect expressions of divorce are originally not meant for divorce. The husband is obligated to provide for his wife, and he is not obligated to allow her to work or to pay her anything in exchange for preventing her. Anger does not prevent the divorce from taking effect unless the person was unaware of what he was saying. A woman's working is permissible under certain conditions.