Actually, being "Italian" would not necessarily have made your ancestors any more "Latin" than my ancestors from Hispania.
"Latin" only refers to the inhabitants of Latium.
The Latins (Romans) then went on to conquer the rest of Italia that consisted of the Sabines, the Oscans, the Volscians, the Umbrians, the Etruscans, the Ligurians, the Faliscans, the Messapics, the Venetics, the Raetics, the Celts of Cis-Alpine Gaul and the Greeks of Magna Graecia.
Most of Italia and Hispania was populated by "Latins by conquest" except for the actual Latin conquerors that settled in the conquered regions.
Mexicans later became "Latin by conquest by the Latins by conquest".
The fact remains that the Mexican mestizo speaks a language that was passed on (with evolution) directly from the Roman Legionnaire to the Hispaniensi to the Castillian Conquistadors to the Mexican Indians and is therefore a language that traces it's roots directly back to ancient Latium.
The Italian American who only speaks English has broken that linguistic link.
Bronze Teruncius of Capua, Campania, Italia, circa 216-211 BC, with Oscan legend.