Stew Driller asked "My question is whether this situation is unusual. Should her name have appeared on my grandfather's certificate or should she have been issued one at the time? How did a minor prove his citizenship. I guess the same question applies to wives before 1922."
I can only tell you that my father completed a 3 page application for a certificate showing that he had derivative citizenship. He submitted his school record and his parents marriage certificate as proof with the application.
My father did this in 1944(age 33) and his father had become a citizen in 1924. The actual certificate he received stated it was derivative citizenship. According to the form, one could receive derivative citizenship by reason of Naturalization of my father/mother Marriage of my mother to my stepfather Marriage to a citizen husband Naturalization of my husband during our marriage Resumption of citizenship by my mother.