What is the religious ruling regarding a wife who disobeys her husband while he is traveling, invents lies on his behalf, and reveals the secrets of his home?

A wife's obedience to her husband in what is right is obligatory. Her disclosing your mother's secret and lying to you is disobedience from two angles: disclosing a forbidden secret, and disobeying her husband. Her fabricating lies about you is a forbidden falsehood and disobedience to your prohibition. As for swearing by divorce, scholars have two opinions: its occurrence unconditionally (the view of the majority), and its non-occurrence if intended as a threat, along with the necessity of an expiation for an oath (the view of Sheikh al-Islam Ibn Taymiyyah). If the anger was severe at the time of swearing, to the extent that you were unaware of what you were saying, then the divorce does not occur; otherwise, it does.