Does divorce occur if the wife leaves and lives alone after her husband tells her: "If you leave and live alone, then you are divorced," and then he retracts that and tells her: "Leave and live [alone]"?

Intention is considered in the husband's oath. The preponderant view is that intention specifies the general and restricts the absolute. So, if he intended by his oath to prevent his wife from leaving the dwelling absolutely, he would be in breach if she leaves. But if he intended to prevent her at a specific time or without his consent, then he is not in breach except by what he intended. The majority of scholars hold that divorce occurs upon breach of an oath of divorce, while Ibn Taymiyyah disagreed with them. Therefore, your husband should personally consult specialized scholars to clarify his intention and act according to their fatwa.