Where to go mid-March?

Florence. Not only is it a fascinating city, it has a huge number of indoor sites if the weather is inclement. Plus there are plenty of day trip possibilities if the weather is nice.

Any one of those would be great. I lean toward saving Naples until you can do the whole area justice, but it's basically a flip a coin kind of situation! I would peruse things to do in both and see what stands out to your group.

Either Florence or the Naples area will be fun. Florence has the benefit of being pretty compact - you can stay in the center and walk to everything. With the Naples area things are more spread out so it depends on what you most want to see.

We rented a car and spent 4 nights in Pompei; we toured the Pompei ruins one day, drove to Positano and Sorrento one day, took the train to Naples for a day trip one day, then visited Herculaneum and Mt. Vesuvius after we checked out before driving north. It was January, so there were no crowds or traffic. The other approach would be to stay in Naples and take day trips outward. Naples has been described as “gritty”, which I now understand to be a euphemism for “everything covered in graffiti as high up as you can reach”. It reminded me of the South Bronx if that area had been extremely wealthy 300 years ago. I’ve been a lot of places but I found it unsettling and was glad we didn’t base there.

Anyway, as I said either place will be fun. Good luck with the trip!

Florence. Great gelato.

More importantly, birthplace of the Renaissance, western art and culture. Lots to talk about and explore with your daughter.

So much of that great art - frescoes and some sculpture - will be in churches. And can never go on the road to museums. A far better introduction to Italy (along with Rome) than Naples, in my view.

Very walkable. Florence is not as big as Naples, and so it is more accessible for an introduction to travelling in Italy.

Florence. We were there about the same time of year in 2023 and the weather was fairly mild and, as noted, there are many many things to see, and many are indoors. You need more time to do justice to Naples, etc., so save that for another trip.
Ideally you could fly into Florence and out of Rome, but if you fly round trip to Rome, take the train to Florence first, then end in Rome. Assuming you're arriving from the U.S., you won't have to worry about being too early for check in at your accommodations (resulting in the jet lag zombies), and Florence makes for a more relaxed entry to your vacation.