Her other family is not paying her "guaranteed hours" for those hours their children are in school, yet expect her to drop everything when they need her (like a sick child home from school.) Or, maybe they HAVE been paying her for those hours, to guarantee her availability, and she has been "double dipping" by working for you.
Either way, obviously she does not see those hours as "yours" guaranteed--and you need to find someone new who CAN guarantee them for you. In return, you need to guarantee that she will get paid for those hours, regardless of whether or not you need her, as well.