I think with the 4 of you, a car makes the most sense. We have done only one trip by train, and really like
the freedom of having a car.
If you can change reservations in Tuscany and CT it would split up the trip a little time wise and make your
path a bit more direct. But don't worry about it.
Furore is a beautiful village with a wonderful beach.
The only reason I suggested Sorrento is because of ease of ingress and egress. Also agree w/Zoe,
Vietri sul Mare has beautiful ceramics, great food, very picturesque and a beach where you can look for shards of pottery.
My daughter has lived in the Naples area for the last ten years. We have visited 7 times. It's one of my
favorite areas of Italy.
Use http://www.viamichelin.com/ for route planning. Don't forget to add fuel and tolls to your car rental.
I'm including the bus schedules just in case it's too busy to drive. I've only been there in April/ earlyMay and
Sept./Oct. We have not had any problems driving during those months. Think you will be early enough
to have some traffic, but not too crazy.
http://www.summerinitaly.com/planning/transportation_amalfi_furore_naples.asp#From Amalfi to Napoli (5.30 - 11.30)
http://www.theamalficoast.net/orari_sita_bus_timetables.html
Have a wonderful time