I can't think of an example in a Latin text (I can in Greek, but that's no use). English is the only language I know in which you can repeat "great" and people will understand -- they don't understand if you try it in French! So. In Latin you have avia for grandmother, proavia for great-grandmother, and then what? My instinct is to say "avia meae aviae", the grandmother of my grandmother (or, in the other case, "avia mei avi", the grandmother of my grandfather). That is in fact the way it was done in ancient Greek.
Avia is the usual spelling of the word, but ava is also possible.
Seriously, this is the funniest use of Latin words I've ever seen. But yes, I think the repitition is best choice, avia aviae meae or proavia proaviae meae