In regards to whether a driver could take you from Positano to Pompeii...yes, quite easily. You could even hire a driver to pick you up in Positano, take you to Pompeii, wait while you tour it and then take you on to Naples. It all depends on your budget. I've done a lot of complicated "budget" transfers. As I get older, they lose a bit of their appeal. For my upcoming trip, I've hired Aldo Limos to pick us up at the train station in Naples and drive us to Positano via Herculaneum. Three days later, they'll drive us back to Naples. 220 Euros, cash, roundtrip. Waiting time at Herculaneum is 35 Euros per hour. I might have done public transport for all of this if I'd been staying somewhere other than Positano, but this is the end of our trip, Positano is our "relax" final destination and I really wanted to stay there specifically.
Expensive? Yes, but I get to split it with my travel companion so that helps a bit.