Itinerary help

I would save Florence for a future trip--otherwise a nice plan becomes a bit compressed.

I would use one of your Sorrento free days for Pompeii instead of going there on your way. It’s an easy train ride from/back to Sorrento. Our South of italy tour spent at least 3 hours (forgot the exact) at Pompeii and we didn’t see it all. A good guide at Pompeii is money well spent.

As much as we love Florence I'd have to say skip it this trip. You only have 12 nights- trying to squeeze 3 locations-all with a lot to see/do- into 12 nights will not be relaxing. Florence is too far/too much as a day trip from Rome.
How old is your son? Would he really enjoy lots and lots of art museums in Florence?

I agree with just going to Sorrento- do Pompeii on its own day- maybe head to Naples afterwards for a pizza?
Not sure if Mondo Guides www.sharedtours.com are running yet but they are excellent. We did Capri and Pompeii with them and loved both. The tour of Pompeii was a full 2 hours, we then stayed another hour and still hardly scratched surface. We only left because it was raining so hard.
They also do an Amalfi Coast drive with stops in Positano, Amalfi and Ravello- that would be money well spent and put all of that on its own 1 day. Might also be nice to have others along to give you and son other people to talk to.

Rome- you will need to prebook entry to both Colosseum and Vatican. I would put something less taxing between those 2 days. Vatican is overwhelming and exhausting and so is Colosseum--especially in the heat!
I'd opt for a food tour over cooking class for some serious fun.

Same thing in Sorrento- 1 day tour, next day rest

Day 6 travel to Sorrento and see Pompeii along the way

What do plan to do with your luggage?

Trying to squeeze Florence into this trip leaves you with lot of travel, and little 'being there' time.

I agree with everything that has been said… skip Florence for this trip and just concentrate on Rome and the amalfi coast. Also agree with putting a low key day between Vatican and colosseum, both are a lot more walking than you think and a rest between would be appreciated. Also, we really enjoyed Herculaneum as well as Pompeii, if you can fit it in. Much more detailed and interesting in my opinion and I would travel to your hotel first unless you have a rental car to keep your luggage. Also an idea… we did a day where we drove the amalfi coast, then ended up at some awesome Greek temple ruins - I think it was called paestum and that was a great day! But again, I think a rental car is needed. You will have a great time no matter what!

There are two places to store your luggage at Pompeii, the first is at the Pompeii Scavi station.
Left luggage is located downstairs between the platforms (depositi Bagagli) cost is €8. The other is at the site itself, but if busy they may be full.