Hello Debra, and welcome to the boards,
You have a lot to cover here so I'll give my opinions on what you should consider.
I'd recommend a day in Rome just to get your bearings and take care of practical issues and then at least a few days to see some of the highlights of Rome. There is more to see than you possible can so make a list and see as many as you can.
From Rome you'll probably want to head to Naples [~1.25 hours by train] as a base for Herculaneum and Vesuvius tours. Naples is a gritty, big city so plan accordingly and don't miss the Archeological Museum.
From Naples there is a small local train called the Circumvesuviana that passes Pompeii and ends in Sorrento [~1.25 hrs].
Sorrento will be a charming break from the big cities and is a good base for Pompeii and the Amalfi Coast. Allow an entire day for Pompeii and you will probably still not be able to see it all. Your ferry options to Almafi will be limited in February but you can always take one of the buses that travels the exciting coastal road.
Here's where I might make an alternate suggestion from this pretty typical schedule. The city of Salerno has good ferry service to the Amalfi coast. If you were to do Pompeii from Naples [~30min train] you could then train to Salerno [~1.25 hours] and use that as base for the Amalfi coast but is also was the main landing point for the Allies in WW2 in western Italy.
https://destinationwwii.com/operation-avalanche-salerno-italy/
Another suggestion is to travel from Salerno to Montecassino (Cassino train station) which you can do by train on the way to Florence. There are several tours you can take that revolve around the Battle of Montecassino and tours of the Abbey of Montecassino can be scheduled.
The train from Montecassino to Florence is about 3 hours and you will change in Rome to the fast train to Florence if you are going all the way through.
So far you haven't listed anything that can't be done by public transportation - mostly train, and then bus or ferry/boat. If you have some specific battle site or memorial then you may need to rent a car or hire someone to take you there. If you lay out the specific sites you're interested in I'm sure you'll get advice on the best way to connect them all together.
Hint: You really do not want a car in any large city like Florence if you can avoid it so I would plan as much driving into one section as possible and then rent a car and return it as soon as you don't need it and then resume large city visiting.
Hope that helps, have a great trip,
=Tod