Depending what time your flight is, being in Sorrento the night before
may not be the best plan
I'll agree with this, Whitney. If your flight is in the morning, you'll want to stay in Naples. That said, check out the Curreri coach shuttle that runs between Sorrento and the Naples airport.
https://www.curreriviaggi.it/en/naples-airport-shuttle
See the Leaning Tour. (Yes, he knows it's not that big of a deal but
he wants to see it. We'll arrive late morning, wander Pisa, spend the
night, and take the train to Rome.)
As someone else suggested, you might consider moving on to Rome versus staying the night in Pisa. I'd like to see you have another night in the Eternal City so that you have 3 FULL sightseeing days to cover ground.
... I was hoping I could convince them to make a stop off there
(Pompeii) to appease the Mom who is planning the whole ding dang
thing.
Ya THINK? The Chaos Coordinator absolutely should be appeased where Pompeii is concerned! The excavation is a historical treasure. Tell 'em they can just sit with the ding-dang luggage if they pout. Yes, it's absolutely possible to do this en route to Sorrento if that gets Mom her ramble amongst the ruins. IMHO, their lack of interest in the thing is just another reason not to use your limited time in the region to backtrack to Naples for pizza.
If you haven't found it yet, here's Pompeii's official website:
http://pompeiisites.org/en/
The scavi is VAST so you'll only be able to explore part of it over a couple of hours. The website provides a printed guide to the excavations in English that you might want to browse before you go as it'll give you a grasp of the functions of various structures, and interesting details about Roman life in an ancient city that was built on top of one even older. Here also is a map that'll give you an idea of the size (and this is only what has been excavated to date).
http://pompeiisites.org/wp-content/uploads/A-Guide-to-the-Pompeii-Excavations-2.pdf
http://pompeiisites.org/wp-content/uploads/Pompeiweb2023.pdf
Capri:
No need for a tour there, if you were considering one. It also has a good website for exploring things to do.
https://www.capri.net
We didn't do the grotto over our 2 nights on the island and have never been sorry. Some folks have enjoyed it and that's fine - we're all different! - but for the scant few minutes the little boats spend in the thing IF they can even get into it, + being hassled for tips, it wasn't worth the time and $ for us. I would scroll through some reviews to see if it's something you really want to do; experiences have certainly been varied! :O)
https://www.tripadvisor.com/Attraction_Review-g488299-d195537-Reviews-Blue_Grotto-Anacapri_Island_of_Capri_Province_of_Naples_Campania.html
I will recommend the chairlift from Anacapri to the top of Mt Solaro, and some of the hikes around the island. We especially enjoyed hoofing it up to Villa Jovis, although if your companions aren't interested in Pompeii, they likely won't be keen on poking around the remains of an emperor's villa either. Great view from up there, tho.
https://www.capri.com/en/e/the-villas-of-tiberius