What is the religious ruling on the action of a daughter who lied and swore falsely to her mother with the intention of pleasing her, after the mother confronted her about actions the daughter admitted to committing?

Intimidating your mother to bring her back to the right path is considered an act of righteousness towards her, and what you did is good and rewarded. There is no sin upon you for swearing a false oath to please your mother, because scholars have permitted it to achieve a benefit or avert harm that cannot be realized otherwise. There is no expiation required for you regarding these oaths because they are "yameen ghamoos" (a false oath sworn deliberately to usurp someone's right), although scholars differ on this matter. The best approach is to resort to "al-ma'arid" (euphemisms or double meanings).