Summer Italy Itinerary

Welcome to the Forum!
A few questions /thoughts-
Is the 19th the day you're flying out, or arriving in Rome? I'm confused which days are your travel days. It's a little easier planning by nights. For instance, I can't tell if you're traveling to Venice on the 29th or 30th? (Venice really needs more nights.) Moving to new locations takes half to three-quarters of a day, in addition to the exhaustion factor.
I think you have one too many locations, and because of the heat and overcrowding, and the difficulties getting into/out of, I would skip the Amalfi Coast. The infrastructure has been sadly neglected, and moving about just takes time and patience. One really needs at least three full days to justify the time and energy of the travel. If you skip the AC, you'll have more time in your other locations, which I think your group would appreciate, especially in the heat and humidity.
I'm assuming you know that 2025 is the year of the Pope's Jubilee, which is expected to bring millions more visitors to Rome, (and possibly Florence.)
I also would strongly advise firming up the itinerary asap, sticking to three locations. So, whatever you choose, book lodging asap, especially for your group size. Also, you will need air conditioning.
You're looking at some beautiful areas, and you'll be making great family memories on this trip! Enjoy!

https://www.glencanning.com/2024/10/31/the-crowds-of-rome/

Easier to fly IN to Venice than out of so I would reverse the order
Skip Naples/AC-too much travel time involved

How mamy nights do you have in Italy?
Count your trip in NIGHTS

It looks like 11 nights-if so 3 locations

Venice should get 3 nights
Florence 2 or 3 plus 1 night for every day trip

Rome needs minimum of 4 nights

Fly home from Rome

All easily done by train

Tuscany hilltowns best with a car-will you rent car and drive ?

If you can nab a late morning flight on the way home from Venice you should be fine. The reason people say to fly into Venice is because flights tend to depart early morning and taking a water taxi from your hotel to the airport is costly.
I’m assuming you arrive in Rome on Jul 19. Don’t expect to sight-see on arrival day because it’s all about settling in. Don’t assume you’ll sleep on the way over either so expect to feel jet lag. Stay on your feet the day you land but skip visiting museums. Rome is a fabulous city to get lost in. You need three nights to see Rome and if you add Vatican City make it four.
You could take a direct train from the Roma Termini station to Napoli Centrale (1h 15m) and visit Naples as a day trip from Rome: https://www.trenitalia.com/en.html. If you do this add an additional night in Rome. You do not have time to see the Amalfi Coast and not only that, relying on public transportation to get from the coast to Tuscany will take all day. With 13 nights I don’t recommend spending one of the days trying to get from one place to the next.
From Rome you can take a direct bus to Siena (3h) and sleep in Siena to explore the Tuscan countryside: https://lovefromtuscany.com/scenic-drives-in-tuscany/. I highly recommend renting a car for a day and driving along the very green and hilly Val D’Orcia and stopping in Pienza to explore its old town before moving on to Montepulciano. If you do this sleep in Siena three nights.
From Siena take a direct bus to Florence (1h 15m). I feel you need three nights in Florence. You can then take a direct train from the Firenze SM Novella station to the Venezia Santa Lucia station (end of line). You need three nights for Venice. One day to see the sights by following the crowd and the next day getting lost. I also recommend taking a vaporetto (water bus) from one end of the lagoon i.e., as the train station to San Marco square or even further at twilight. This way you’ll see the palaces that line the Grand Canal fully illuminated and not the decay on the exterior.