Tuscany>Amalfi Coast>Rome OR Tuscany>Rome>Amalfi Coast

Since you fly home from Rome finish the trip with a few days in Rome and avoid the rush back the day before, which wastes a day of the trip. so I'd do Tuscany first, then head for Positano by car or by train dropping the car in Positano if possible or at a train station like Naples. It might be fun to travel from Sorrento to Naples by ferry -- we did that -- don't know if there is ferry service to Naples from Positano. Then take the train back to Rome and finish there.

The train does not go all the way to Positano. Your best route depends on whether you have enough days to see and enjoy Rome in total. The important thing you have not yet learned is how much time it takes to get to Rome from Positano, plus allowance for delays along the way. Use the search box on the desktop version of this site. Many posters have followed your route.

If you are flying out of Rome I would end there BUT if you can fly out of Naples ; then I would prefer Tuscany, Rome and Amalfi last and take a private driver to take me from lodging in Positano to the Naples Airport which is very easy to do and not that expensive.

Transportation time from Positano to Napoli Capodicchino is probably well over an hour by private transfer; from Roma Termini to FCO is about 35 minutes. I generally like to eliminate one pack/unpack by spending my last few days in the city I will depart from.

If you don't want to drive in the traffic of the Amalfi Coast, then I would drop the car at either Salerno or Sorrento, each of which are starting points for the SITA buses to Positano. You can reach Salerno entirely by highway, while entering Sorrento requires some time on local roads that can get more traffic.

I see no benefit to spitting Rome into two, separate stays.

Yeah, Laura, that's actually the best idea so far. Find a place to drop the car, hopefully near Salerno's Centrale station, which serves for trains & buses. Then take the SITA bus from Salerno to Amalfi, which is just under an hour, then right at the station--really, it's a parking lot right on the coast--change buses for another hour to Positano. Not sure whether you can buy both tickets at the Salerno station, but I think you can.

I would definitely drive all the way from Tuscany to Positano (about 5 hr drive, mostly freeway except the last few miles where the road is a two lane highway, curvy and narrow as you approach Positano).

Positano has limited parking. Make sure you find accommodations that have parking arrangements (either on hotel premises or affiliated garage). I find taking the car to Positano a better option compared to public transportation (provided you secure parking with your hotel). That will avoid having to transfer to multiple means of transport (trains, buses, etc.) with luggage and all.

After Positano, drive back north to Rome and return the car upon arrival (no need for a car while in Rome). On the morning of departure take a taxi from city hotel to airport (about 30 min drive).

Always leave the city of your departure as your last stop.