changing planes in FCO, 2 different tickets

You'll have to go thru both Immigration and Customs. That means collecting any checked bags and then going to the Alitalia counter to re check them, since you are on 2 separate tickets. That means leaving the secure area, then going back thru security. But you have 3 1/2 hours, which should be plenty ( if you arrive on time).

Thanks, CJean. Will we need to go through customs if we don't have any bags to check at Alitalia?

I did this a few years back. I had only my carry on, so didn't have to go outside security to claim bag. However, I knew my carry on was over Alitalia's size limit so I looked for a transfer desk as they have in some airports. I couldn't find one, so I went to an information desk. The man told me, "Take your carry on on to the plane. Alitalia will lose your luggage." Well I braved it, got it on the flight to Sicily and all went well for me. But, others on my RS tour weren't so lucky. Their bags were lost for several days. They had a great attitude about it though and eventually they did get a change of clothes. If your sister does check be sure she carries at least an extra set of underwear and an extra top in her carry on. I have made this a rule for me ever since that trip.

To piggyback on the advice of Laurie Beth, I always carry a change of underwear, nightgown, and clean top in my carry on bag, and, of course, toothbrush, and meds. Baggage delays are not peculiar to any one airline. In my almost 50 years of flying, I have experienced a few, not many, but a few. Best to plan for the worst.

To add to other responses...You will be coming into Terminal 3 and the Alitalia flight will be leaving from Terminal 1. The terminals are connected, and according to at least one person above that has been through there, if you have no checked bags, you should be able to stay airside and not go through security. If you check bags, then you will have to reclaim outside the secure area and go back through security.

As for immigration, yes will will need to go through immigration as long as FCO is your first stop in the Schengen zone (ie: direct flight from the US or via London)

This is all so helpful! Thank you all so much. Glad to know that we can likely stay airside, even if changing terminals (which isn't always the case, eg JFK). I also appreciate the reminder to have toothbrush and change of certain clothes, etc., in our carryons, especially because we might be forced to check our roller bags at the Alitalia gate. To have such useful answers, so quickly, is great! Hurrah for this forum, once again!

Going through immigration between our flights at FCO was in a special area for transfers and only took five minutes at most. FCO is a nice airport, with some good food options too.

But for future reference it is never a good idea to assume that you will arrive on time. 3 or 4 hours of your precious layover time can be eaten up in the blink of an eye with delays and cancellations and long lines.

Yep, Tim, you are right. We decided to risk it because there is only one flight a day to Trapani, with a (scheduled!) 3.5 hour layover, and the price was low. Worth a gamble? However, if we miss that flight, there are also hourly flights on Alitalia to Palermo, so we'll pay same-day price (which still doesn't look to be too much) to Palermo and then take a bus or shuttle to Trapani. But yes, we will be gambling.