Which Are the Days of Abstinence in Lent?

They both are. The Church nowadays requires abstinence from meat only on Fridays of Lent, so your father is obeying the current discipline. In the early centuries, Christians fasted and abstained on Wednesdays and Fridays—not only in Lent, but all year long. So your mother is honoring this ancient tradition.

The spirit of Lent is to do something more, something extra, to grow closer to Christ. The Church sets some guidelines as a minimum, but we are free to do more. Traditionally, the penances of Lent are fasting, prayer, and almsgiving. Each person, together with his confessor, decides on what practices will best prepare him for Easter.