Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
No doubt that the obedience to one’s parents is one of the most important matters in religion. Allah linked His Right of being thanked to their right and He linked the order to deal with them kindly to the prohibition of Shirk (polytheism). Allah Says (interpretation of meaning): {…..give thanks to Me and to your parents, unto Me is the final destination.}[31:14]. Allah also Says (interpretation of meaning): {Worship Allâh and join none with Him in worship, and do good to parents,….}[4:36]. He also Says (interpretation of meaning): {And We have enjoined on man to be dutiful and kind to his parents,…..}[46:15].
The mother is more entitled to be obeyed than the father.
Al Bukhari and Muslim reported from Abu Hurairah that the Prophet (Sallallahu Alaihi wa Sallam) said when a man asked the Prophet (Sallallahu Alaihi wa Sallam): "Who deserves my good companion more?” The Prophet (Sallallahu Alaihi wa Sallam) replied: “Your mother, then your mother, then your mother, then your father”. While the mother is to be obeyed in Islam, obeying her is unlawful if she orders the child to do something forbidden by Allah. Al Bukhari and Abu Hurairah reported from Ibn Abitalib that the Prophet (Sallallahu Alaihi wa Sallam) said: “No obedience is in committing sins. Indeed the obedience is in righteous deeds".
From the above, we conclude that if your secrets are peculiar to you and their disclosure will not result in any harm, if your mother orders you to tell her, you must obey her. But if these secrets are concerning others who entrusted you, then you should not disclose them even to your mother as long as any harm could be caused by that act. As keeping such secrets becomes then an obedience to Allah which is given priority over obedience to mother.