The Child Abuse and Neglect Prevention Act of 1982 defines "child abuse" as: "harm or threatened harm to a child's health or welfare by a person responsible for the child's health or welfare, which harm occurs or is threatened through nonaccidental physical or mental injury[.]" See MCL 722.602(1)(b).
By this definition and assuming your version of the facts is accurate, your father's actions wouldn't seem to be abusive. However, your mother may have a different version of events. Or your sister's injuries may warrant a different opinion. Ultimately it will be up to the prosecutor to decide whether to prosecute.
If your father already has a lawyer, he needs to consult with him and listen to his lawyer's advice. Unless and until the prosecutor decides to file charges, there is not much your father can do.