Are there things we can't take into Italy from the US?

There are rules which you can see by searching for 'Carta doganale' and reading a 38 page pdf in Italian. I scanned it and I didn't see anything an ordinary tourist is likely to carry - which accounts for the lackadaisical attitudes of the customs folks at Italian airports. Just avoid bringing your relatives any elephant tusks and you should be ok.

Will you be clearing Customs in Italy or an intermediate country?

You are asking about taking dates into Italy. Probably OK if your spouse isn't the jealous type.

Chile restricts importation of all fruit, whether fresh or dried, so that accounts for your dates. This is not unusual for countries in the Southern Hemisphere. Australia and New Zealand are very strict about fruits and vegetables.

Italy has no such prohibition so your dates ( assuming they are the plant variety, not human) should be fine. But you cannot bring any animal products ( meat or dairy). But fish, although it is an animal, is allowed if it has been filleted and processed ( no whole fish allowed). So something like Northwest-style smoked salmon pieces should be OK. I have taken vacuum-sealed shelf-stable packages of smoked sockeye salmon as gifts to various countries ( after checking customs regulations) and they were always well-received.

I am enjoying the sense of humor many of you have shown! Thanks for that ;-)
Our dates are the fruit variety from a date palm tree in Indio, CA! What I should do is ask the family if there is anything from the states that they would like! I can't remember the name of the last person to reply but that was an excellent summary for me. We will be flying from LA to PARIS where we change planes, then on to Florence! I forgot about the quick stop in Paris where we will have to pass through immigration. Oh dear.

Quick aside: our first time going to Italy a few years ago was very similar. When we got off the plane late at night in Milan, we didn't go through any sort of customs. We were afraid we had missed something. Later, we realized that since it was part of the EU,our stop in Paris took care of the customs stuff. The flight from CDG to Malpensa was considered a local one so no customs required. Lesson learned and I should have thought of that when I posted last night!

Customs in Europe is not like customs in the US. In Europe, there are no forms to fill, you simply choose to walk through a green or red door, depending on whether or not you want to declare items. In my experience, customs isn't even always manned. I guess you could be spot checked, but I have never seen this happen (I've probably walked through green channels a few hundred times).

Haha, Norma! Good one.