Could your wife be convinced to take a smaller suitcase for this portion of your trip? Perhaps you could arrange to store most of her luggage in Civitavecchia or Rome.

Traveling by any means with a LOT of luggage is very difficult. I wish you well, and I hope your AirBnBs don't have a lot of stairs, no elevator, etc. Book a large taxi or car service to take you to FCO for your flight home.

FWIW, I don't trust GPS options (phone, in-car, whatever) that promise to avoid ZTLs. But, in any event, I don't like or use Waze... even at home in Los Angeles, the Land of Traffic.

It might be worth mentioning to your wife that "in Europe we are having washing machines" but what will be will be. Have a great holiday.

I would rather drive a Swiss alpine pass than the Amalfi coast. Some Italian drivers are CRAZY.

We had a car for our trip to the Amalfi in 2012, that was before the odd/even thing and it was October so not high season. We picked it up in Sorrento and dropped it back there at the end of the trip. The roads are super narrow, twisty and scooters and motor bikes use the center line in both directions no matter how twisty etc or what is coming in the other direction. Sometimes when a large bus came around the corner from the opposite direction we had to back up so they had room to make the turn. My husband is a good driver-calm and has great spatial sense, he found it challenging but very enjoyable. I still have videos on my phone of our road adventures, I think I gasped and swore at five minute intervals. We rented the smallest Fiat, which my 6'3 husband managed to fold himself into. You want a small car because parking is at a premium there and often the spots are just literally on the side of the road with just enough space to put a tiny car.

We did enjoy having the car for the freedom it gave us and didn't run into any issues. If your wife has that much luggage you will likely need to fold the seats down in your rental, for sure do not stop anywhere and leave your luggage unattended.
Have a great trip.