How many days in Florence vs. Amalfi Coast?

Sounds reasonable assuming you both are ok with walking a lot on uneven surfaces.
Florence warrants many days usually becuz visitors see many museums there, however u say that is not your interest. Pisa, Tuscany are nearby to Florence for day trips if you see everything u wish in Florence. BTW sorrento is a great base but also a wonderful place to walkabout, enjoy views and cafe scene.

Naples area (Amalfi, Sorrento, Pompei, Capri, etc.): 4 nights minimum
Florence alone: 3 nights
Florence plus side trips in Tuscany: 3 nights for Florence plus 1 night for any Tuscan day trip.

Flight check on www.skyscanner.com. Where you are coming from is not indicated, but a Florence/Naples flight could be doubtful.

If a Rome FCO round trip is necessary you take the train from the airport to Florence [Fiumicino Aeroporto to Firenze SM Novella]; direct at 10:53 and 13:53, others you change downtown.

Florence to Napoli Centrale, then downstairs at Garibaldi for one of the Sorrento trains, getting off at Pompeii Scavi [where there is baggage storage]:

https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule

https://www.sorrentoinsider.com/en/campania-express-train-schedule [less uncomfortable, mid-March to mid-Oct]

Back to Napoli Centrale for Rome, train or driver from the hotel.

Since you are planning on visiting Pompeii en route, why not stay on the Amalfi coast? There are also ferries to Capri from Positano, and if you are interested more in Paestum, then staying toward the mainland end would make that a shorter day trip.
I think your Florence and Rome day allotments look good, so unless you can add days to the trip, something has to suffer--in this case Amalfi coast time.

I have been to Rome twice, spending about 12 days there and still haven't seen everything. Plan on at least 5 nights.
4 days are good for Florence. Recommend not driving in Italy, take a train to Sienna if you want to go on a day trip.

Sorrento is a good place for a base. One day for Capri, one day for Pompeii and One day for Amalfi Coast.

If you do 5 in Rome, 4 in Florence, that leaves you a bit short (2 days) for Naples area.

I am taking an open jaw flight from the US, arriving in Naples and leaving from Florence. The days of arrival and the departure are in addition to what I've shown so, I will technically have an additional night (and half a day) in those two cities.

I like the idea of Sorrento as a base since it's easier to get to/from.

Roberto and geovagriffith, if I'm not misunderstanding something, what you posted seems to match the tentative schedule I posted, considering I'll technically have an extra night at Florence and Naples.

I might just budget an extra hotel night so we can have some flexibility if we decide to adjust the schedule on the fly.

While it is not true that Rome and Florence are the same, for someone who says they are not interested in art museums, they have some similarities. I suppose the biggest obvious differences are Vatican City and the Roman Forum. It sounds like you already have your tickets (and it's impressive that you got flights into and out of "secondary" cities.) But I would have suggested something different for someone who has never been to Europe, especially in shoulder season. I mean a second country.

Is your mother of Northern Italian extraction, and that's why you picked this itinerary?

Pompeii is a very special sight, but so is Venice, and it's good for several days.

I plan on getting the tickets in a few days, and I'm going to add a couple days and leave out of Venice.

I'm open to suggestions on other countries. I thought a lot about it, but for two weeks moving around that much might be difficult, and I've been to many of the nearby countries. I'm all ears for suggestions though, especially which Italian cities to cut out.

My mother is of Croatian descent, but I was just there last year and she has no real connection to anything there.