Italy in August

I suggest flying into Venezia, good first look at Italy for your son and good to relax after flying.

Then go to the Amalfi Coast/Sorrento, so that Roma is your last stop; fly out of FCO.

The heat and humidity can be challenging. Make sure you stay hydrated and plan to cross the street to walk in the shade whenever possible in Roma.

American Airlines flies Philly to Rome direct (ex Wed), so I would suggest you take advantage of that ...

Straight to Sorrento (4nts) after landing in Rome
Fly from Naples to Venice (3nts)
Train to Rome (3 nts)
Fly home from Rome

Check the AA price difference between simple Rome return and open jaw - direct to Rome for Venice connection, and back home from Rome.

You should be very careful choosing hotels on your trip--making sure they're going to be air conditioned. And it does get hot in Central and Southern Italy in June, July and August. But sometimes you've just got to suck it up and not worry about the crowds.

I assume since you mentioned Philly, that's where you're going to be flying out of. The only direct flight is on American Airlines into Rome FCO, and that's where I'd suggest you fly into and out of. You can make train reservations out of Rome Termini up to 120 days out on Trenitalia.com to get the cheapest fares and make reservations for the fast trains.
I'd suggest visiting Venice first, Rome second and the Amalfi Coast third--coming back into Rome the day before your flight.

1) Yes, it is the busiest time of the year, therefore book hotels as soon as you can.

2) American airlines flies from PHL to VCE in summer and also from PHL to Rome-Fiumicino (FCO) all year around.
So the easiest flight is

Going:
PHL-VCE
Return:
FCO-PHL
All with American Airlines.

Although Sorrento/Amalfi are south of Rome (near Naples), it is a good idea to leave your departure city for last in your itinerary:

Therefore I would (assuming 9 nights on the ground):
Fly to VCE (see above)
Venice 3 nights
train straight to Naples (then commuter train to Sorrento, which will be your base)
Sorrento: 3 nights
Back on the train north to Rome
Rome: 3 nights
Fly to PHL from FCO.

Perfect. Even better as Roberto suggests above, direct to Venice ...

WED 9 AUG 2017
AA714
18:45 Philadelphia(PHL)
09:10 +1 day Venice(VCE)
Travel time 08h25m, Non stop

THU 10 AUG - Venice (3nts)
SUN 13 AUG - Sorrento (4nts) - days out to Pompeii, Positano, Capri
THU 17 AUG - Rome (3 nts)

SUN 20 AUG 2017
AA719
11:55 Rome(FCO)
15:55 Philadelphia(PHL)
Travel time 10h00m, Non stop

I agree with David's post above about your itinerary.

Air conditioning in Europe is not the kind we have here. Air here in the states can cool a room to the 60s. Most I have come across I have come across in Europe will cool the air temp 10 or 15 degrees, never reaching what we are used to in the states. When researching hotels, check the reviews about air conditioning. My last time in Rome it was like an average July day in Georgia hot and humid.

I take American from Philly to Italy every summer (a couple of weeks before you). For your son, the special part of flying into Venice would be the tremendous view of the alps followed by a stunning view of Venice. After all my trips, these sights still thrill me. Venice is great for several days - there is plenty to see plus you have the other islands each with its own history to share. Yes, it will be hot but the Italians have a wonderful thing called the "riposo" - an afternoon rest. It will allow you to skip the worst heat of the day and emerge more refreshed for the cooler evenings.

You can get to Sorrento fairly easily by train - making the ride a part of the vacation and not just a nuisance. Train (the fast train, the Freccia) from Venice to Rome then on to Naples. You may have to change in Rome but I'm not sure. Plenty of countryside to see and the train is very comfortable. From Naples I like taking the ferry across the bay to Sorrento - again, it becomes part of the vacation. The Amalfi Coast and Capri can be very crowded but I'm sure you can deal with it. :) Trying taking the boat from Sorrento around to Positano and Amalfi Town. It's been a couple of years but I remember one boat that stopped along Capri and let everybody jump off for a swim. Can't do that in Philly!

Pompeii, Herculeum and Paestum are great day trips from Sorrento. The Greek ruins in Paestum are especially impressive.

I fly home from Rome, American flight #719 (at noon so your morning isn't so rushed). There are certainly plenty of historical sites in Rome to keep your son busy and wide-eyed I'm sure. Ostia Antica is a great day trip from Rome if you haven't had enough of your ancient Roman ruins. Honestly, I like roaming around there more than Pompeii.

As you probably know, the Italians eat late in the evening - that's when it is the coolest. It's also the time where everything really can slow down and people just enjoy being outside. I notice that even the tourists change their pace and just sit at a cafe or by a fountain, and pretend to belong. For me, that's the best part of my time in Italy.

Enjoy your trip. Your son is very lucky!

Another thing your son might like is Acqueduct Park; there's also a section of the ancient walls that can be walked.