Is my mother required to make up the fasts she missed in previous years due to her fear of bad breath after her divorce, knowing that she thought repentance and commitment to acts of worship would absolve her of making them up?

The mother must know that intentionally breaking the fast in Ramadan is one of the major sins. If she repents, she must make up the days she missed fasting, as this is a debt upon her. The correct view is that expiation (kaffarah) is not required of her except for breaking the fast through sexual intercourse. If she does not know the number of days, she must investigate until she is reasonably certain that her obligation has been fulfilled. According to the majority of scholars, she must feed a poor person for each day she delayed making up the fast.