I did this trip almost 3 years ago. Did not have the option at that time to fly through Rome from IAH, but if I was doing it again, that is what I'd opt for. Alitalia just started a non-stop route from IAH to FCO. I've looked at the options to get to either airport in Sicily using that airline, and it's MUCH better than what we had to do.
We landed in Palermo through Frankfurt and returned from Catania because that was the best itinerary, both for logistics on the island and for flight options. Coming home, I had to buy a stand alone ticket on a budget airline from Catania to Milan. So, the round trip flight (booked through United, but with some Lufthansa flights) was IAH -> FRA -> PMO and MXP -> ORD -> IAH. Dealing with the Milan airport when arriving on a "regional" plane but needing to catch a major international flight was a real PITA.
I'll paste a link to my "trip report" below.
https://texags.com/forums/54/topics/3355286It was just two of us, so I can't help with the logistics of going with a big group. We rented a car, and I found driving to be very easy and enjoyable.
The thing is, the best things to see in Sicily are kind of spread out. We did Scala dei Turchi and the Valley of the Temples, which was about a 2 hour drive from Palermo (we did not spend any time in Palermo). From there, we did a 2 day cooking school at a farm near Vallelunga and Valledolmo. Then we made our way to Cefalu and finished the trip in Taormina. We did a day trip to Etna from Taormina with a local tour company. It was a decently far drive. The Catania airport is also a decent drive from Taormina (but it's much closer than Palermo).
We stayed in Airbnbs in both Cefalu and Taormina. Both experiences were really great, but both Airbnbs were a bit outside of the city center. We could walk from our apartment in Taormina to all the main attractions, but we needed a car to get around Cefalu.
I do think you would be hard pressed to find a lot of Airbnb options that can hold that many people; however, you may be able to find a house or villa to rent. There are a couple of websites out there (beyond Airbnb) that cater to Europeans. Villas of Distinction, Sicily Luxury Villas, and The Sicilian Villa Company, to name a few. When I was looking, renting a house was pretty affordable, but it usually required a week long stay, and we did not stay in any one place for that many nights.
With that many people, I'd see about finding a tour agency that can book you a bus with a driver to take you around.
As the previous poster said, figure out what things you want to see most. Cefalu is a fantastic beach town, albeit nothing like beaches in the US. Taormina is on the water, but I would not really call it a beach town - it's more akin to the Amalfi Coast. There are some great agriturismos and wineries in the central portion of the island. We didn't make it to Syracusa and Noto, or anywhere in that southeast portion of the island.
From Cefalu, I paid a boat captain to take us to one of the Aeolian Islands for a day trip. This is a whole other wonderful experience, and you can actually do multi-day charter cruises to the various islands. I would love to go back someday and do that.