A USA notarized document has zero recognition in Italy. Absolutely none at all.

A USA notarized document would only be of use if you think that the authorities in the USA are going to take your children from you or block your travel. Once the plane takes off, it is of no use.

If you want a notarized document written in the USA to be of any use in Italy you have to go to the US Consul and have it authorized, translated into Italian, registered etc. A notary from the local bank branch won't do.

And it's all unnecessary. Considering all of the divorced and inter-ethnic families that travel to and from the USA you will have no problem in Italy because virtually all mothers have a different last name from their children. Many of them look different from their children because with the surge of immigration in Italy almost 15% of marriages are now inter-ethnic.

It doesn't raise an eyebrow when an inter-ethnic child with a different last name is traveling with her mother in Italy. Of course, if you have had a divorce and share custody with an ex-spouse you should obey the divorce decree. However, thinking that a letter notarized at FedEx is going to help anything on the Italian side is not true. And it is wrong to suggest that Italian passport control is sitting there racially profiling millions of people traveling with children.