Car drop off

The driving advice is not just about curvy roads with no guardrails. Brutal traffic, and busses that have to stop, backup, and make another go of a curve, on a two-lane road, are equally important factors. You also need to know whether your hotel has parking in Positano. There is little street parking, and in high season, even less. Even in Sorrento (which closes certain streets every night ... ) we saw cars lined up and stationary waiting to get into underground parking lots on the outskirts, in the evening. (We spent five nights in Sorrento, and used a private car and driver to get back to the Naples RR station, after using the hot, crowded Circumvesuviana to get to Sorrento. But I'm not urging you to stay in Sorrento. It's not the same as Positano. We stayed in Sorrento for easy daytrips.

The SITA busses, which run roughly half-hourly, are jammed all summer. I would describe them as reliable, but with double the passenger load they are designed for. You might wait for two busses before you can get onto one. There is less public transportation after dinner.

Are you familiar with the geography of Positano? There is only a single, two-lane road through the town, and hotels can be hundreds of pedestrian steps from the road - setting aside the parking issue. Your decision is also tied into your departure day, and how long you have to get to your ... ? flight?

The closest place you can drop the car off would be Sorrento. But then from Sorrento to Positano you need a bus or an expensive taxi ride.
Since you have a car already and maybe you plan to use it after visiting the Amalfi Coast, you could also keep it. The big problem there is parking not driving. So if you keep it make sure you talk to your hotel about parking arrangements. Most have arrangement with local parking lots. The cost is about 25-30€ a day, and with an hotel arrangement you generally have in and out privileges (and possibly a small discount). With my friends we often left it parked and used boats or even buses during the day. The car is convenient to have to get there and to get out (basically first and last day) especially for a group like your and luggage. It’s also convenient if you decide to go out to dinner outside of Positano, because bus service at night ends early. During the days there you won’t need the car much. Parking scarcity and traffic congestion, especially in July, will likely convince you to leave it at the parking lot while you go around by bus or boat.
But call the hotel about parking arrangements, because those lots book up in July. I’ve never been there in July and August, so if you keep it, make sure you have a place to park it at night. If worse comes to worst, just use the car to drop off luggage and family at the Positano hotel, then head back to Sorrento to return the rental.

Driving along the Amalfi coast is a challenge because of the traffic. The road is fine.

I have been on much worse, scarier, roads on Maui.

( and re-reading Roberto's comments would not hurt)

Thank you all, for your great advice. We are super excited about this trip! Our hotel has private parking and we may just leave the car there and use public transportation for our daily excursions.

Thanks!
Jun