Itinerary

I think staying in Sorrento makes more sense than Positano as a home base. Pompeii, Herculaneum and Capri are much more easily accessible from Sorrento. While Positano is beautiful, personally, more than a day there would be a bit boring for me, although it all depends on what your goals are.

You will want to visit Pompeii and Herculaneum as early in the day as possible at that time of year, because it will be very hot, and there is not much shade to be found.

Naples is one of the more densely populated and intense cities in Europe and will also be sweltering.

We spent 4 nights in Sorrento and enjoyed it very much. I could see spending 6 nights there but I think 12 is too many. You'll get tired of all the travel to see other towns on your list.

I would split between Sorrento and Amalfi. Not Positano. We spent just a few hours there and that was enough for us. It's also not a transportation hub as Sorrento and Amalfi are. There is a ferry in Positano but inclement weather means it doesn't run. There is a bus but in July those buses are going to already be full by the time they get to Positano going in either direction. If you don't mind 3 locations I'd add 2 nights on Capri. It was nice as a day trip but would be much more enjoyable as an overnight or 2.

From Amalfi you can visit Ravello easily, Positano easily and you might consider a day trip to Paestum to see the Greek temples.
From Sorrento- Pompeii and Herculaneum are easy but do go early- it will be brutally hot and there is no shade.

Consider Sorrento 5, Capri 2, Amalfi 5