What is incumbent upon me if I later learn that my mother was not paying Zakat on the money she gave me?

If the mother states that she has paid the Zakat, her word is to be accepted. If, however, it is presumed that she made a mistake, then Zakat is obligatory upon her due to her ownership of the wealth, and she must pay it herself or appoint you to pay it on her behalf. Your paying the Zakat on her behalf without her permission is not sufficient, because Zakat is an act of worship that requires intention. The mother must also be just among her children in giving gifts.