Is it permissible for an elderly woman to go to a Qur'an memorization class without her mother's knowledge, especially given her desire for reward, her knowledge of the place's safety, and her mother's fear?

If your going to teach women the Quran is safe from any harm or suspicion, then the first step is to try to convince your mother. If she refuses, there is no sin in going without her knowledge. Sheikh Ibn Baz permitted a girl to go out for da'wah (preaching), visiting relatives, and visiting the sick, with modesty and chastity, even without her father's permission, as long as there is no danger in her going out that would necessitate her father's permission and consultation.