Well, it's possible. It's true that there are a huge number of Ivaldi families in N.Italy, N.France and Argentina. But I would not say it's like Smith.
The hard part is tracing ancestry. I haven't found a researcher who can hunt Church records and make 3 or more generations back for me.
Your story didn't sound familiar, except for a young daughter who died at a young age. Different circumstances i believe.
I wish I could help more.
- Davide