I do remember my grandfather Attilio Ivaldi telling us that the Ivaldi last name in Itlay is like Smith and Jones here very common last name.
You might try the Catholic Church from where you ancestor is from. The keep Baptism, confirmation, marriage and death records of families in that parish and I would try that if you are having no luck finding anything.
On one of my Grandfather's trips to Itlay her brought back a bottle from a brewery back in Itlay run by Ivaldi's. My brother sitll has the bottle. That was when he told us that the Ivaldi last name was very common back there.
Joy Ivaldi Durrett