Capri vs Amalfi , from Rome

Neither one has a "one seat ride" option.

From Rome you can take a train to Salerno, then a bus (or in season a boat) to Amalfi.

From Rome you can take a train to Naples, then a boat to Capri.

You can start by looking at Rome2Rio for times and some companies that run the transit, then look at their websites to confirm schedules: http://www.rome2rio.com/

All that said, I can't imagine a less relaxing day to schlepping to either of these places from Rome for just a day. I went from Naples to Sorrento and Positano for a day, and consider it largely a waste of time. These places are for settling into, not seeing quickly. The thought of the extra time it would take starting from Rome instead of Naples...means that this would be miserable for me, unless you were going to spend at least a few days once there.

I would agree with Harold: both of these locations are too far away to comfortably do in a day from Rome, and I can't imagine that it would be a 'relaxing' trip at all. You also have (last I looked) only 3.5 days planned for Rome, which is barely enough to scratch the surface of that one so I wouldn't cut time even shorter to try and do this.

I have to agree with the others (and I'm someone with a high tolerance for long day travel). Amalfi and Capri are really best reached from Sorrento, not Rome. Also, I don't know about you, but (a large part of) Italy may not be an ideal location to swim because the coastline is very rocky and I've yet to see a beach my feet can step in (no smooth sand like the beaches of CA which I'm used to). I think that's why Capri is full of hotels with swimming pools.

Doesn't sounds relaxing to me.
Too far to do a day trip, especially Capri which is an island you do realize so you need to get to another city/town and then catch a ferry and back to even get there.
The related issue is I don't envision public transport toward Rome leaving these towns that late in the evening, you really need to allocate at least an overnight stay if not 2 nights if you want to make this happen.

Most of the Amalfi coast beaches are pebbles, not sand, and on the small side. Do you care about that? You also have to consider the date of your trip. The trains are very cheap three months in advance (one specific train on the ticket, only) , not so cheap later. And this area can be very congested from May to August. You might not get on the ferry you hope to take because of the crowds. +1 for not doing it as a day trip.

People do make the majority of this route as a daytrip if their goals are to visit Pompeii, Herculaneum, and/or the Archeology Museum in Naples. That's different from adding the further transport issues of Capri or Amalfi.

The last one-hour fast train back from Naples to Rome departs at 19:30 most days except Saturdays, with later trains being a bit slower. If you've gone down the Amalfi coast and ended at Salerno, the last train back to Rome is at 19:45.

How about from Florence to Cinque Terre? I agree with you guys about Capri and Amalfi. I research about Cinque Terre. I could stop by Pisa after Cinque Terre on the way back to Florence. Is it a good idea?

That's better but I thought that was already covered in previous threads?

https://community.ricksteves.com/travel-forum/italy/cinque-terre-c057e6ef-5a64-4f15-ad29-c551ad715fcd

https://community.ricksteves.com/travel-forum/italy/from-florence-to-cinque-terre