If you want to see some of Rome and Florence than why not split the stay between Rome and Positano???
From Rome, Florence can be reached via fast train in a couple of hours so works as a day trip.
You may be able to work in a stop at Pompeii on your way between Rome and Positano.

Positano is a wonderful destination (at least minus the crowds it is) but it makes a god awful base location!
Expect crowds to be absolutely awful in late July / early July everywhere on the Amalfi Coast. The place is Super popular now with Americas on vacation.

Make sure to take a daytrip boat to Capri and visit the town of Ravello during your stay in Positano.

As mentioned above about not leaving valuables or anything at all visible in a parked car. That would be true in Naples but also true absolutely everywhere in Italy!
Lastly, driving on the Amalfi Coast is definitely not for everyone and I don't recommend it in late June / early July for multiple reasons (parking being the biggest one)