Is my mother required to make up for the Ramadan fasting she missed when she was thirteen and a half years old due to her ignorance and her father's ignorance?

Your mother must make up the days she missed in Ramadan (definition) if she reached puberty (by menstruation, wet dreams, growth of coarse hair around the pubic area, or reaching 15 years of age). Ignorance is not an excuse in this case. In addition to making up the fasts, she must offer expiation by feeding a poor person for each day if she delayed fasting those days until another Ramadan began without a valid excuse.