Am I obligated to fulfill my oath to my mother not to visit her for three months, knowing that she told my father the secret despite my stipulating that there would be no expiation if she did so?

You must visit your parents and expiate your oath, because the Prophet, peace and blessings be upon him, said: "Whoever swears an oath and then sees something better than it, let him do what is better and expiate his oath." Your refusal to visit them for three months is an unlawful act of disobedience. And if you stipulated not to expiate in order to magnify the matter, then that is of no consequence, and you must break your oath. However, if you swore not to expiate, then two expiations are incumbent upon you: the first for breaking the oath, and the second for not fulfilling the first oath.