Of course the whole point of an organized tour is to have the arrangements done for you. But your friend could (if comfortable with independent travel) stay at Pompeii, or visit Herculaneum (by local Circumvesuviana train and foot) while you all go to the Amalfi Coast. The van or bus could pick them up on the way back to Rome.
Note that this is a VERY ambitious day trip from Rome. There will be an annoying amount of time on the vehicle, and not enough "free time" at the sites. Before I paid for this, I would ask how much time in Pompeii. That's because most independent travelers spend 2-4 hours in Pompeii, and we often read posts from those who enjoyed the entire day. We didn't see Pompeii until our third time in Italy, and we slept in Sorrento.
The highway from Rome to Sorrento is pretty ordinary. It's from Sorrento to the Amalfi Coast that's curvy, and as noted, slow. At least there's lots of sky and fresh air, and the road is well paved. The car has to stop when traffic bogs down as busses arrange to pass each other a curves where the two-lane road isn't wide enough.