Just got back from four days in Sorrento. Did Pompeii and Herculaneum one day (drove to both). Did Amalfi and Positano another day (drove the Amalfi coast drive). Did Capri one day (boat from Sorrento).
Driving is "interesting." If you are a really good and careful driver (which I consider myself to be), it's doable. But it's not fun for the driver. Fun for the passengers, with great views.
Positano -- can highly recommend a lunch at Buca di Bacco Hotel restaurant. It's right on the main beach in Positano. Had a great lunch there (one of the best I have ever had). Hotel looks pretty solidly booked in mid-Sept. though.
Have only ever driven there the two times we have been to the Amalfi Coast, so I can't help much on alternative transport.
I will say that I was quite glad that I happened to get upgraded to a Volvo with automatic on our trip. I drive a manual well, but it would be a really challenging drive in a manual car.