Storage of luggage for early arrival in Rome on airport departure day

You could store your luggage at Roma Termini train station and take the Leonardo Express train to the airport.

Or if you plan to take a taxi or car service to the airport, this prior posting has links to baggage storage services that have locations in various parts of Rome: https://community.ricksteves.com/travel-forum/italy/luggage-storage-at-rome-termini. Maybe you could find a storage location closer to the places you plan to visit with your daughter.

One last thought is that the private transfer from Sorrento to Rome will already be expensive, so maybe inquire about the incremental cost of having the car drive you around Rome and then to the airport. Who knows. Maybe it wouldn't be that much more expensive and it solves your luggage storage dilemma.

That sure doesn't leave you with much time. If you go with the recommended 3 hours before departure and the ~40 minute ride from Rome, plus the 3 /12 hour drive from Sorrento to Rome, I don't see how you have any time in town.

What time do you expect to leave Sorrento?

I see you are a new poster. It sounds like you've been to Rome before. Is that true? When is your trip? Are you locked in to staying the last night in Sorrento? If you really want to show her a site or two, you could travel the evening before and stay in Rome. You could get an early start the next morning and squeeze in some activities before heading out. That way your hotel could hold your luggage for you before heading to the airport.

In addition to the timing issue - and a car service from Sorrento to central Rome is going to be very expensive - I'm unsure what showing your daughter the major sites means, exactly? You are not going to get inside some of the most "major" of them without advance, timed-entry tickets.

If it's just getting a look at the outsides, then the suggestion to just pay your driver to take you around a bit is a good idea. He will not be able to get you directly TO all of them, depending on which ones they are. Even better would be just staying in Rome the night before.

Figure at least 7.5 hours or more of your day is going to be eaten up just in transport + the requisite 3 hours you need to be at Fiumicino before your flight (assuming this is an international flight and you are departing from there).

One last thought is that the private transfer from Sorrento to Rome will already be expensive, so maybe inquire about the incremental cost of having the car drive you around Rome and then to the airport. Who knows. Maybe it wouldn't be that much more expensive and it solves your luggage storage dilemma.

Considerations may be worth it.

If you decide to store your luggage at FCO, of course you need allowance to retrieve it -- check it or however you decide -- and your arrival check in.

From FCO to Termini Station is about 32 minutes. From there, you could walk to some attractions.

Maybe you could focus on one attraction and neighborhood for your day visit.

About 30 minutes from FCO, is the "Monti" neighborhood/Colosseum -- providing no traffic of course. The district has some artisans, interesting cultural attractions -- coffee bars, restaurants, shops. Check out via Urbana

You "might" be able to secure regular floor tickets through -- https://www.coopculture.it/en/it/colosseo-e-shop.cfm, -- if you can get them for your date, and roam around the Colosseum. A regular visit is about 60-minutes.

Going deeper into Rome's city centre (to other major attractions) might be iffy -- depending on the day you arrive, time of day, traffic, anything going on in and around the streets.

Even if you have a private car, they can only go "in" so far - ZTL prohibitions, pedestrian-only streets, etc. You would still need to walk some - not that bad - but time is ticking on your clock, lol.

So "you could" see a couple of attractions if you plan it right -- mapping it out to make the most of your time.

This 10-minute vid will give you an idea of the "proximity" of the major attractions. Some are not as close you think. https://www.youtube.com/watch?v=V2VcEkPaeF4 "Rome In A Nutshell"

Also, check out The Roman Guy -- Monti neighborhood. Hidden Gems of Rome: Monti in a Day -- https://m.youtube.com/watch?v=g4XCIANUSXc

Sean, one of the leads for the company, gives a nice explanation and peek into the neighborhood.

There are other videos on Rome's neighborhoods by The Roman Guy.

Enjoy!

Almost forgot....
If you intend to store/retrieve your bags at Termini, add more time: their facility can be very, very busy.

Another option is stasher.com - they list businesses in major cities who will store bags by the hour / day. This might be handy and you won't have to wait in line at a large storage facility.