We just finished an annual stay on the Amalfi Coast and you couldn't pay me to drive a rental car there. June is not shoulder season, in May the AC is already packed. We have rented cars at Salerno for travel to the Cilento Coast and Puglia, but arrange for private transfer to AC from there. Two weeks ago, our driver told us how crazy it already is this year and foreigners don't understand how bad the traffic is. There are plenty of YT videos that show how crazy it is to negotiate turns/buses/tunnels on the narrow roads. Also, the Amalfi Coast is best appreciated from the sea. There are plenty of ferries from Positano to Amalfi, Capri etc.

You definitely don't want a car in Rome. The official taxies have a flat rate from FCO if your accommodation is within the Aurelian Walls. Otherwise, Romecabs is highly recommended for private transfers:
https://www.romecabs.com