Recommendations on how to get from Sorrento to Rome's FCO airport?

Here is a summary of choices

https://www.rome2rio.com/map/Sorrento/Rome-Airport-FCO

Personally, I would go to Rome the day before.

How large is the 'group'. ? The more you are the less nimble you are

Unless you’re going to arrange a private driver, there is no way I would try this on a fly-back day. There’s too many moving parts, one missed connection, one slow train, one flat tire, one strike (they happen) and you’re sunk. Stay the night before in Rome, and enjoy your last hours in Italy with peace of mind.

Good advice about spending the last night in Rome.

I'd just take the circumvesuviano from Sorrento to Naples, catch a fast train to Rome, and enjoy my last afternoon and evening there.

Here is another vote for going to Rome on the day before the flight home.

To clarify why everyone's telling you to go to Rome on the 12th -
You have to take the Circumvesuviana commuter train (tram) to Naples. The ride can take as long as 1.25 hours, the trains run about every half hour and they can be late. Then you have to go through the train station to get to the train to Rome (another 1.25 hours). Then you have to take another train to the airport - that runs twice an hour and takes about 1/2 hour - and delays are not infrequent. So you have up to 3 hours of actual travel time, plus possible long connection times. You should be at the airport by about noon. That means leaving the Sorrento hotel as early as 7 am and worrying about delays the entire morning. If you spend the night in Rome, you have plenty of time in the morning for breakfast and a final walk around town, then take the 30-minute train to FCO. If there's a problem with the train, you can take a taxi. If your group is more than 2-3, a taxi from the hotel is probably the same price as the train tickets.

And, as a plus, you could leave your bags at/near the train station in Naples and spend a few hours at the acclaimed National Archeological Museum seeing the original art removed from Pompeii, then continue to Rome for the evening.

Last August I stayed in Ostia as a jumping off point for my flight out of FCO. The Rome Metro connects to a commuter line which terminates in Ostia, just below FCO. I made a deal with the B&B owner to run me over to the airport for an early morning flight. Your flight is 3:10 so probably no need to stay out by the airport, but just adding this in the event it is useful to someone here. Great Roman ruins also in Ostia at "Ostia Antica", the ancient sea port for Rome. But that's another topic.....