Well the stop over is included on the AA ticket as well isn't it? At least i know it was when i did new york to berlin (AA/BA) with a lay over in london
so if i booked the trip as new york to rio with a lay over in buenos aires, wouldnt that all be included as one trip?
and i'm not trying to collect miles on this trip, i'm planning on using them to fly it, since the san diego leg in particular is pricing out at over $1000 at this point