Does my telling my father to tell my wife's father, "His daughter is divorced," constitute a divorce after the marriage contract and before consummation, due to problems with her family, and because I wish to mend the matter?

If you instructed your father to inform your wife's father of her divorce, then it is considered a valid divorce as soon as it is uttered, and it does not require witnesses or writing. If you have not consummated the marriage with your wife, nor had a legal privacy with her, then the divorce is an irreversible (bā'in) one, and she is not permissible for you except with a new contract. However, if you had a legal privacy with her, then you may take her back before the completion of her 'iddah (definition) (waiting period).