It would have been useful to have the month of the year, since ferry schedules and general crowding are seasonal. If you are going this May (2017), you will be lucky to get your fifth choice of hotel.
As noted, Vesuvius is in the opposite direction from the far, far away Paestum. That day schedule is destined to fail. Look at Google Maps.
You have made a huge commitment to the AC. That's fine, as long as it's what you want. I don't think it's worth that amount of time, but huge numbers of posters here, U.K. and otherwise, would disagree with me. (I've been to Sorrento twice, total five nights.) Perhaps I can concisely explain my reservations by observing that you are going to pass a different outlet of the same international soap/cosmetics/luxury leather/lady's accessories/jewelry franchise on each day. How many of them do you need to see?
Do you have any idea how much time you plan to spend in Pompeii? How will you travel to Positano? It makes a difference, but the roads are always jammed up in high season, and there is no other way to get to Positano.
Edit: If you use the desktop version of this site, it has a Search box and you might find a couple of posts from people who both managed and failed to arrange "Paestum from Sorrento".
We paid our Sorrento luxury hotel's local travel partner 240 Euros for an 8-hour car and driver to visit the Amalfi Coast as a day trip. That might not be enough time for you, but we saw (with free time on foot) Positano, Amalfi, Ravello, and drove through two smaller towns.