Rome to Sorrento

Take the train from Roma Termini to Napoli Centrale. It is super easy and fast. Take whichever train fits your schedule the best and has the best price. You should buy tickets at least a few months out to get the best prices. I've always traveled with Trenitalia, but I know others use Italo when more convenient.

I too prefer Trenitalia’s website https://www.trenitalia.com/en.html over Italo and recommend taking the nonstop train from Rome’s Termini station to Napoli Centrale. You can then take a taxi to the port and take a ferry to Sorrento.
The other option is to hop on the Circumvesuviana train downstairs at the Napoli Centrale station. I’ve been on this train before but not with luggage. The problem with this commuter train is you’ll be riding with pickpockets.

This website has all the info you’ll need about trains in Italy
www.maninseat61.com

Buy your tix from the official sites
trenitalia.com
Italotreno.it

Both have apps as well
sign up for Italo newsletter for discount codes

You want Napoli Centrale
Afragola is a bit out in suburbs

"No stop" is Italo's (quite stupid) marketing name of Milan-Rome-Naples hs trains that make no intermediate stops between Milan and Rome.

Is there a difference between the Italy EVO and Italo AGV?

Like saying the difference between Boeing 707 and 747.

But, is it more convenient to just get a driver to pick us up at our
hotel in Rome and take us direct to our hotel in Sorrento?

You'll get to Napoli Centrale by high-speed train much faster than by road. Then take advantage of that convenient, complementary car service from there to your hotel, if you wish. A word about "curvey roads"? If you suffer from motion sickness, take your preferred anti-nausea meds in time for them to work before getting into a vehicle from Naples to Sorrento. Been, there, done that, only from Sorrento> Naples Airport, not that it would make any difference. I was pretty green by the time we got there. 🤢

The same will be true if you intend to explore the Amalfi Coast region by road, and you'll also be dealing with the height factor as well.

If you are meeting a limo in Naples anyway, you might as well pick a high-speed (like Frecciarossa) train that cuts over an hour off the trip from Rome to Naples. Advance discount ticket is not changeable or refundable in that case, but you have a car to meet.

I cannot speak for someone with motion sickness, but there is a world of difference between the road trip from Naples to Sorrento and the road trip from Sorrento to, say, Positano. Both have plenty of traffic, with pauses and stops. But the cliffside road ON the AC is the one that's really vertiginious. I would not work yourself into a state over the Naples-Sorrento segment because it's just not that bad.

Note that a Mercedes sedan (typical car service for Sorrento hotels) would be quite crowded for 4 with luggage. You might know already whether (if they send) a van is better or worse for your motion sickness.

You may not understand that the (downstairs by escalator from the Rome train in Naples) Circumvesuviana train to Sorrento is operated by a local transit agency as a commuter service, like an urban subway or surface transit. It tends to be VERY crowded and sometimes not air-conditioned. It is intimidating to people with no public transportation in their home lives. It has only shoulder-bag luggage racks and it's hard to get full size suitcases on when the train is jammed. We were happy to pay the Ambasicatori's car service partner 90 euros to go back to Naples, especially since the Sorrento cab to the hotel was a rip-off 15 Euros for a short ride.

I would not work yourself into a state over the Naples-Sorrento
segment because it's just not that bad.

Tim, for sure there's no need to work into some sort of state but as someone who has dealt with car and motion sickness all of my life, I know what it is to be miserable...and I was miserable on that route. An ounce of prevention in the form of Dramamine or similar would have been welcome had I known in advance. Car or van, makes no difference if I'm not in the front seat, and even that isn't always a fix.

I'm assuming when the OP meant they're not good with curvey roads, that might be the issue. Then again, maybe they just don't like curves for some other reason.

Kathy, I have been seasick on ships many times, and can get carsick while reading on curvy roads. I'm one of four children and I have much experience with the others having to sit in the front seat. You are mistaken in suggesting that I am cruel or unsympathetic to the OP. Here's one quote:

"Some individuals experience great anxiety as symptoms of motion sickness develop or even before by virtue of prior exposure or impending exposure to a provocative motion environment. (Jacob et al. 1993, 1995; Money 1970; Money et al. 1996; Yardley et al. 1994). This interrelationship has been recognized since very early times. Balaban and Jacob (2001) have provided a comprehensive review ..."

from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4112051/

A less scholarly or peer-reviewed statement is:

"A person who has experienced motion sickness in the past may have worse symptoms on future trips by expecting to feel sick." from https://www.betterhealth.vic.gov.au/health/healthyliving/motion-sickness

Tim, I didn't say nor suggest that you were cruel or unsympathetic to the OP. I know you're not. Just sounded as if you weren't bothered by something that could (and did) bother someone else. I didn't expect that particular route to do number on me so it wasn't power of suggestion. Maybe we look at things differently but I'd rather be informed up front about something that could make me feel lousy rather than find out when it's too late to do anything about it.. But 'nuff said.