Taking my Mom to Italy :)

since you fly in and out of Rome-Fiumicino (FCO), I'd probably go to Naples first thing after landing by train, then after the stay in the Naples area (Naples or surrounding areas, like Sorrento is up to you), I'd end the trip in Rome for a few days. By doing so you save yourself one city and hotel transfer. Basically you have one hotel in the Naples area, and one in Rome.

Train timetables are below:
www.trenitalia.com

Enter station names in Italian:
FIUMICINO AEROPORTO
NAPOLI CENTRALE

From the airport all solutions with require a train change at ROMA TERMINI (for high speed FrecciaRossa trains) or ROMA OSTIENSE (for InterCity trains). FrecciaRossa trains take 70 min from Roma Termini to Napoli Centrale. The Leonardo Express from Fiumicino Aeroporto to Roma Termini take 32 min and departs every 15 min. You need a minimum of 10 min for the layover at Roma Termini.

I cannot speak to the sites on Ischia but overall this seems a reasonable plan based on your interests. Personally, there is never enough time in Rome and you could maybe skip Ischia and just make the trip about Naples and Rome and be perfectly satisfied. Could you make one less transfer by doing a daytrip to Ischia from Naples? Fewer transfers = more time enjoying.

Be sure you go to the Pantheon. The Parthenon is in Greece. ;-)

Thank you for the train tips and catching my mistake :) I will look at switching the order to maximize our time

Going from Rome to Pompeii, do you carry all of your belongings with you, or can you check them at the site?

On Ischia, you might want to visit La Mortella Gardens. We loved Negombo, the thermal park.

I returned from a one week stay in Ischia last week, having had an amazing relaxing stay. Although we did not go to the cavascura thermal baths, we went to the Poseidon Gardens and stayed from 9:45-5:00. Your trip sounds busy, but wonderful. I hope you get to do all you are planning. Enjoy!

Since you'd have already seen Rome, you might want to consider spending the last night or two in Ostia which is only 15 minutes to FCO. It is a lot cheaper than staying in Rome and it has a MUCH quieter pace and vibe. And if you're not worn out from all the other sightseeing you might enjoy the ruins at Ostia Antica. It is much like Pompeii without the drama of Vesuvius, and without the heat and crowds (it has a lot more shade.) It is a perfect last place on the itinerary to wind down before flying home.

Flying home from Rome pretty much requires you to sleep in Rome the
night before.

Central Rome is about 45 minutes from FCO, through brutal Roman traffic, and costs about €55

Ostia is about 15 minutes from FCO with moderate traffic and costs about €30

So why are you REQUIRED to sleep in Rome the night before? There are more convenient options.

Sounds like a good trip and mix of sights. Agree with Roberto’s advice to do Naples area first and finish with Rome. That will also allow you to do Pompeii as a daytrip from Naples, which will be a lot easier than taking your luggage there all the way from Rome, storing it at the site, and then lugging it back to Naples on the Circumvesuviana train which is not ideal for that. I’ve been to that area twice and have never heard of any of the places you mention for day 7, not of course that that means they’re not worthwhile, as it’s good to include some things not as much on the beaten track. Herculaneum is amazing and quite different from Pompeii as another alternative if you’re not over-ruined out, but it is difficult to fit these both into a short trip, as they really can’t be properly done on the same day — I’ve seen both but on separate trips to the region decades apart. I haven’t been to Ischia either but it sounds like a good choice, especially compared to the alternative of over touristed Capri (I loved a day on Capri, but that was on a quiet January day many years ago). In Rome, looks like you intend St. Peter’s but not the Vatican Museums (Sistine Chapel), which I assume is a deliberate choice, and that’s fine if so, you can’t see everything and the other museums you mention in Rome are all excellent. Having pizza in Naples is iconic and of course you should do that, but the pizza in Rome is just as good.

Having pizza in Naples is iconic and of course you should do that, but
the pizza in Rome is just as good.

I have to respectfully disagree. Perhaps it is possible to find true Neapolitan pizza in Rome, but for the most part the pizza you get in Rome is no better than you'd get back home.

Nothing wrong with respectful disagreement. Rome has a somewhat different style of pizza that I personally like just as much as Neapolitan. Sicily also has its own style which is excellent. Regarding pizza at home, there are a number of places in the Washington DC area where I live that serve genuine Napoli style pizza which is just as delicious as anything you can get in Naples — but admittedly it seems like it’s better in Naples because, well, you’re in Naples.

RE: pizza in Italy.

I just never had any good pizza in Rome. Now granted I didn't make it a mission to track down great pizza, I just ordered it occasionally in whatever restaurant I happened to be in and it was just "okay."

On the other hand, I've had pizza in New Jersey that was just as good as anything I ever had in Naples. And to this day, one of the best pizzas I ever had in my life was - believe it or not - in Edinburgh at a restaurant called Amarone. It was epic, and every bit as good or better than any I ever had in Naples.

I just never had any good pizza in Rome. Now granted I didn't make it a mission to track down great pizza, I just ordered it occasionally in whatever restaurant I happened to be in and it was just "okay."

Next time you are in Rome come back and ask where to seek it. Living there nearly 5 years we had some ordinary pizza as well, but only 3 or 4 places we went back to time after time because they were sooooo good.

If she hasn't seen it yet your mom might want to watch the recent TV 3-part series "Pompeii: Out of Time with Tom Hiddleston"

I highly recommend a guided tour in Pompeii. We went there once on our own, it was so much better when we went back and were on a guided tour. The RS book lists some public ones, if this has long been mom's dream then you might want to look into whether it's worth hiring a guide just for the pair of you