My name does mean "three wives." The dean of my college told me it was derived from the Muslims who conquered Sicily (my ancestral homeland). They were allowed to marry four wive yet never more than three at one time.
Given the short life expectancies and the hazards of childbearing, it wouldn't have been that unusual for a man to have two wives in succession die young and then marry a third one...I know of two ancestors in the US who married for the third time because their first two wives had died (one in the late 18th century, the other in the early 20th century). That may be a more mundane explanation of the name Tremoglie but I would guess more likely.
Sicily is beautiful. I've been to Siracusa and Palermo.