Rome plans

Whew! I would say you have a jam-packed list of sights to see. If that's your traveling style, more power to you. For me, Rome has been more of an experience, just "human being" rather than "human doing." Because I find that the central area of Rome has so many historic and beautiful sights that you're bound to encounter one every time you turn a corner. I don't stress over which ones I've gotta see in a certain time slot. But that's just me; others will have different advice.

WOW, agree with above comment, it's a lot.
There is a great walk starting at Piazza Navona that would easily take you via Pantheon & Trevi Fountain then up to the Spanish Steps and if you really want a longer walk, up to the Galleria Borghese. I would start early at Piazza Navona as there are fewer tourist out earlier. Or do that in reverse, making sure you get to the Pantheon before closing.
I consider the Galleria Borghese to be the finest small museum in Rome, so if you've seen enough art consider something else on day of arrival so you can savor it!
A note about seeing the Vatican Museum and Vatican on the same day. The entrances are a ways apart, so take a look on Google, either of these are pretty overwhelming in terms of majesty and art so that's a very full day if you want to hoof it around from one to the other.
Personally, I think the train station isn't the nicest area of Rome, I would prefer to drop my bags at a hotel and take a passegiatta from there.
We were in Rome for New Year's, 2019 and I researched restaurants & cafes along our route, so we wouldn't be standing on a street corner hungry, which you will be with this itinerary! We tried a number of the places near the sites on the Rome Wise blog, they were all terrific! (NO affiliation, I just love good food and my Italian relatives have taught me to be quite particular!)
Good luck.

The Renaissance art in Florence is vastly different from most of the pieces at the Borghese Gallery. Bernini's sculptures are a world away Michelangelo and Donatello. But it does take time to digest.

Hi there, Andrea -
I'll be the dissenter here 'cause I think your wish list is very do-able for 3.5 days, especially as you've devoted entire days apiece for the Vatican and Colosseum/Palatine/Forum. Trevi Fountain and the Spanish Steps are merely walk-bys which can (and should) be done when the museums are closed, and you'll be just a few blocks from Trevi if staying near the Barberini metro station. I'd suggest doing the Pantheon en-route to the Colosseum/Palatine/Forum on Monday; reservations are currently required for weekend visits and it's possible that mandate will extend thru the rest of the year.

https://www.pantheonroma.com/home/

I might make Sunday your Domus Aurea day + a big walk to cover some of the things you don't have on your list, such as Piazza Navona + some of the glorious churches. Doing D. A. would mean backtracking to this same part of the city for the Colosseum/Palatine/Forum on Monday but doing it on Saturday wouldn't leave you much leftover time for exploring the heart of the historic district. There are fewer attractions up in the Galleria Borghese area so I'd do that on your partial Saturday: remember it will get dark early in December.

With some idea of the sorts of things you enjoy sightseeing, we can make additional suggestions for Sunday?

The Italian national museums are currently not participating in "Free Sundays", and while there has been a recent announcement for "Free Sunday" on August 1 at the civic museums + a few of the archeological sites, it's unclear to me if that will extend to the remaining months of this year. For COVID distancing, they are also requiring reservations for the attractions included.

https://www.wantedinrome.com/news/rome-city-museums-free-on-sunday-1-august.html

I have not been closely following the current Green Pass mandate for entrance to many of the attractions so scan the forum for ongoing conversations around that issue? The same will apply to time-sensitive COVID testing for entry to Italy and back into the U.S, at the time of your trip. This situation is pretty fluid and likely to change between now and 12/2021.

Your plan is very close to how we divvied up Rome:

One day in Catholic Rome (Vatican Museums, Sistine Chapel, St. Peter's Basilica).

One day in Ancient Rome (Colosseum, Forum, Capitoline Museum). For us the Capitoline Museum was a much better day than the Palatine Hill. The Palatine is just more of what you'll see in the Forum - ruins, without much context. The Capitoline was one of the better museums I've seen in Europe. I don't agree with the post that the Museum and the Basilica are far apart. Its true that the entrances are a ways apart, but the self-guided tour of the Museums ends at Sistine Chapel, which is right on St Peter's Square and leads right to the Basilica.

One day in Baroque Rome (Piazza Navona, Campo di Fiori market, shopping on the Corso, Spanish Steps, Trevi Fountain). Also slotted the Pantheon into this day, for geographical reasons, not thematic.

Like previous posters, I would be hesitant to add any museums or tours to that already busy itinerary. Instead use whatever time you have left to go into a church, or sit at a cafe, or get gelato by the Spanish Steps.

....or get gelato by the Spanish Steps.

But don't SIT on the steps or on the edge of Trevi Fountain. You'll be sternly ordered back onto your feet! Using church, fountain or monument steps/terraces in Rome as places to picnic is pretty much forbidden and can result in a hefty fine. Same for other Italian cities.

Thank you all! I didn't realize that it was quite such a busy itinerary so I may re-think but I'm hoping Kathy is correct about the do-ability. The updated info about Free Sundays is super useful; my googling didn't result in anything recent so I appreciate the link.

I like the overall idea of leaving our bags at the hotel on Saturday and meandering our way back over to Domus Aurea. We should be pretty well-rested as our previous days are just lounging in the Tuscan countryside so this shouldn't be a problem. I'm also putting together a rough list of appealing restaurants and will check out Rome Wise on the suggestion above. Thanks again!

... but I'm hoping Kathy is correct about the do-ability.

LOL!! I can vouch for do-ability because we essentially did it on a trip back in 2007: 4 nights; 3.5 days, and that was coming from the U.S. versus Florence. We did substitute some other attractions for Domus Aurea on that trip - as it wasn't yet open to visitors - as well as the Borghese, which we did on a subsequent trip, but covered everything else on your list. Because that one is limited to a 2-hour visit (they clear the museum after every 2-hour time slot) it's easy to know how long it'll take to do it! :O)

Stuff we did on that trip which aren't on your list:
Capitoline Museums
Santa Maria Maggiore
A long walk in Villa Borghese (on arrival day, to stay awake)
Piazza del Popolo/Santa Maria del Popolo (arrival day)
San Pietro in Vincoli
Santa Maria Sopra Minerva
Campo dei Fiori
Santa Maria in Trastevere
Teatro di Marcello/Portico d'Ottavia/Jewish Ghetto
Top of Victor Emmanuel Monument

We walked everywhere - didn't use any public transport on that trip - had multiple coffee stops every day, and were usually done in time for Beer O'clock at around 4:00 - 5:00 PM, although we also started early. So cross my heart, it can be done!!!

But don't SIT on the steps or on the edge of Trevi Fountain.

If that's a rule, its a rule more honoured in the breach. There were hundreds sitting on both the Spanish Steps and the Trevi Fountain.

Well, I pull up Skylinenewswebcam for the Steps now and again just to guess how long it'll take for someone of authority to ask a sitter to get off their tush. In fact, I just watched two of them ordered to standing position while banging out this post! Oops, there goes a third...

https://www.skylinewebcams.com/en/webcam/italia/lazio/roma/piazza-di-spagna.html

No one sitting on the edge (meaning hands or feet could be dangled in the water) of Trevi for long either;
https://www.skylinewebcams.com/en/webcam/italia/lazio/roma/fontana-di-trevi.html

I think they got a lot more strict about sitting/eating on them after both underwent lengthy restorations.

https://www.ctvnews.ca/world/rome-s-spanish-steps-are-not-for-sitting-police-1.4539840

This article is from 2019, but I believe it's still in effect.

No sitting was definitely enforced May 2019

Baths of Diocletian & the adjacent Roman Museum are pretty much must-sees, especially if you're early for a train at Termini. But there are literally 1000 must-sees in Roma.

You ain't kidding about wanting to be in Rome for the entire two weeks. First trip in 2010, 3 days. Last time in 2017, a week at an apartment. Next spring, 6 days at the end of an 18-day train journey to Lucerne, Varenna (Como), Florence, and then Rome. Bucket list--in the next 5 years for sure--an entire winter in Rome!

I would vote for seeing Domus Aurea on Saturday afternoon. I don’t think the light (or lack of) due to it being December will impact your enjoyment as much as it might at the Borghese Gallery. We saw it on our trip in 2019 and thought it was fabulous. It will also give you an additional context for your Colosseum visit. The last time I checked, D.A. is only available for tours on the weekend. I think dropping your luggage first might be nice and your room might even be ready early for check-in.