Itinerary for end of Sept. and early October

Starting in Venice is easier, so keep that. Definitely don't take a day away from Venice. If you have to steal a day to give to Rome, take it from Florence.

You barely have a minimum of days necessary to see Rome. I agree to leave Venice as it is and take time from Florence and give it to Rome.

Yeah, I'd say the same. Give Rome more time. You could get it from Florence or Siena or Sorrento. Leave Venice as is. Are you keeping the car through Florence and Sorrento, or using trains? The car won't be useful in Florence. You might consider the train from Venice to Florence, time there, then the car for Siena and Tuscany and on down to Sorrento and return it near Rome.

See my response here:
https://community.ricksteves.com/travel-forum/italy/train-reservations-for-sept-2022

It would be easier to take a direct train from Venice to the Florence SM Novella station (2h 15m) and make Siena a day trip from Florence (1h 15m by direct bus). To get to the Amalfi Coast take a direct train from Florence to Salerno (4h) and a direct ferry from Salerno to Positano (1h 15m) and spend the night. The next day take a ferry from Positano to Sorrento (45-minutes).

Any hotel suggestions for all locations? $200 - $275.00 Thank you.

Venice-Hotel Ala

Siena-Palazzo Ravizza ( they have parking, fairly easy in and out of town, great terrace with
views)

Rome many great choices in the Pantheon area

Sorrento
Grand Hotel de la Ville (might be over your budget)

Lots of recommendations here on forum, do some searches