As a nation state, Italy has emerged only in 1871. Until then the country was politically divided into a large number of independant cities, provinces and islands. The currently available evidences point out to a dominant Etruscan, Greek and Roman cultural influence on today's Italians.
World War I was waged in Europe from 1914 to 1918. Italy, although it had a treaty with Germany and Austro-Hungary, attempted to stay out of the war. In 1915, Italy joined on the side of France and England.
Many Italians who anticipated the coming problems in Europe left for America. However, once was broke out, I don't know how much immgration was allowed. My grandfather got out before the war, but he wasn't able to get my grandmother here until 1920.
How interesting. My grandparents were married in Italy in 1909 but were in France by 1910. My uncle was born in Marseilles in 1910. I do not know if they returned to Italy between then & the time they immigrated (1914 for GF & 1915 for GM.) I really have no idea why they came to the US.
It sounds like you're saying, though, that the rise of Mussolini might not have been a factor in their decision to leave--family myth to the contrary!
War was probably the reason for their decision to leave. There was only 20 years (1919-1939) between the WWI and WWII. Most of Europe was in turmoil for that period of time. The aftermath of WWI led to the rise of Hitler and Mussolini. Mussolini was a writer and minor official from about 1910 on, so your family probably put it all together.