Travelling from Rome to Pompeii and then on to Sorrento -

I visited Pompeii from Naples, but I see no problem with what you plan to do (other than the weather risk that exists with any date-specific plan). It's round-trips from Rome to Pompeii that are discouraged. Rome-Pompeii-Sorrento requires much less time on the train.

However much one might be interested in Pompeii, the physical aspects of visiting Pompeii make it really tough to spend the entire day there even if your hotel is in the city of Pompei itself. Firstly, it's likely to be very hot, and there's essentially no shade. Secondly, most of the streets in Pompeii seemed to be paved with monstrous cobblestones that are very hard to walk on (be sure everyone has good shoes with thick soles). There are sidewalks, but they are usually way higher than the street, so it's a chore to hop up and down--which you sometimes need to do because the sidewalks are narrow and you will encounter other people.

In other words, I suspect you won't be sorry to leave when your 4 hours is up, however much you've enjoyed Pompeii. Do take plenty of water with you and some easy snacks so you don't have to wear yourselves out going back and forth to the little cafe (or whatever it is; I carried my own provisions).

I think Rick identifies the highlights very well, but you may have extra time, so doing some extra research pre-trip might pay off for you. The visitor center posts a list of what's open every day. It's smart to check that so you don't head off on a wild-goose chase; Pompeii is very large.

We did exactly that. We went to Rome to Sorrento with a stop at Pompeii.

We took a "faster" train to Naples and the Circumvesuviana to Pompeii. There are two Pompeii stops. You want Scavi. There is a luggage check. We stayed most of the day. If you happen to do that, buy your train ticket to Sorrento in advance, and know that the luggage check line may be a few minutes.

We used the walking tour in the RS guide. Also, we watched applicable RS episode and a bunch of YouTube videos before leaving home.

Had we had another day, we would have liked a night in Naples to see the Archeology museum and for pizza.

Sure, it works, baggage storage is the main concern, but there are options there. It is not much of a detour, take the fast train to Naples, about an hour and a half, get on the Circumvesuvia train, the same one you would take to Sorrento, and get off at Pompeii Scavi stop after about a half hour. If you leave Rome a bit before 8 AM, you will get to the site at the 10 AM opening time.

Time spent at the site varies on interest, but figure a solid two hours, three hours to see the main things, four if you are really interested. Some will of course spend up to 8 hours, but the typical person is worn out in 2-3 hours.

When done, hop back on the Circumvesuvia, and you will be in Sorrento in about a half hour...so by 2 PM conservatively.

How early? I likely loved it more than most and spent 10 hours in Pompeii over 2 days while we were based in Sorrento. I'd be disappointed if I felt rushed in trying to see it in half a day. It's only a 40 minute ride from Pompeii to Sorrento. If your hotel in Sorrento will let you leave your luggage, it would be easy to back track.

We spent about 6-7 hours in Pompeii and could have stayed longer. You do need to be prepared with plenty of fluids, sunscreen and a hat. We didn't check out the snack bar/cafe, we brought fruit and "heavy" snacks. June could be nice or it could be hot. It was about 85 in Pompeii when we were there and it does feel hotter when the sun heats up all the rock.

A half day could be fine depending on your interest. I think we arrived at about 10pm from Rome and left for Sorrento at about 5pm.