Is it a sin not to inform the mother about private matters between the spouses, and is this action correct in light of the audacious discussions in society regarding such matters?

If "private matters" refer to issues of sexual intercourse and related topics, then it is forbidden to speak about them, whether to one's mother or anyone else. This is due to the severe warning narrated from the Prophet, peace and blessings be upon him, who gave the example of Satan relieving himself while people watch. This indicates the prohibition of either spouse revealing the secrets and details of sexual intercourse.