What is the Sharia ruling regarding a wife who threatened to kill her husband, then falsely and slanderously claimed she was subjected to beating, and what should the husband do?

What your wife did, threatening you with a knife, is forbidden (haram) because it involves terrifying and frightening, and the angels curse whoever points an iron weapon at his brother. As for her leaving to prepare a medical report, it is not permissible if she has a male doctor and exposes herself to him, except out of necessity and with a mahram. Your wife is disobedient (nashiz) due to these actions and her refusal to return to your home. As for your hitting her, if it was for discipline, not severe, and was preceded by admonition and abstention that did not work, then there is no blame on you for it. However, if you caused her harm, then it is forbidden. We advise you to strive to bring your wife back to your home, teach her the rights of Allah and her husband, and deal with her with wisdom and patience.