LOL. Sorry to be the one to correct you but some things really cannot stand. It was my mother who, as a young married woman, became enchanted with the movie, the location and the romance of the story. In fact, growing up, I remember hearing that song played often during parties or dinners at our home, along with songs or themes from other movies. It was the kind of music impressionable little girls found irrestably romantic. IIRC, I think I first saw Three Coins in a Fountain late one night on TV and no doubt with my mother and probably early on during High School. Of course, I loved it, too... and the Trevi Fountain was one of the first things I went to see the day I finally arrived in Rome.
OMG your mother - My apologies Darlin´ I always think the whole world is as young as I am. I am always surprised to find there are people even younger, but I suppose time flies when one is having fun.
No matter, your first introduction to that movie you were a young High School girl so my all my comments apply.