Is it permissible to hit the husband who is threatening to kill and disfigure his wife and who has abused her after divorcing her in absentia, in order to prevent him from harming her after he caused her to lose her job?

You are not permitted to strike this man. Rather, refer his case to the competent authorities to deter him and punish him if he deserves it, for punishment is the prerogative of the ruler. If your sister is certain that her husband has divorced her three times, she must separate from him, even if through khul‘ (divorce initiated by the wife). If she is certain of the divorce, it is not permissible for her to remain with him.