Hi Karen, I've not been to the Artis Domus, but have visited Residence La Terrazze. The views from this one are absolutely amazing! Did look up the rooms on both, and the second seems much more serene. It also provides a shuttle service into the center of Sorrento and is maybe a block for the bus to Positano and Amalfi.
Beach in Sorrento
http://www.leonellisbeach.com/en/
The bus will get you to the Circumvesuvian in under 20 minutes. Making it easy for you to reach the train to Pompeii and the ferry to Capri and Ischia.
Here is my post on your previous thread with instructions on how to reach Sorrento and beyond.
"Karen, the reason so many posters are telling you to go south first is because your arrival day is usually wasted. You'll better utilize your time, having more FULL days per location. Here's what I'd do...
Day 1 Arrive Rome. Allow 2-3 hours for passport/immigration. Taxi to Rome Termini. With 4 of you it will be less expensive than the Leonardo Express. Train to Napoli Centrale 1hr17min. Circumvesuvian (located downstairs of Naples station) to Sorrento. 1Hr15m.
4 Nights Sorrento. Can only recommend this hotel, Since we usually stay at my daughters home north of Naples. http://www.booking.com/Share-3huZLd
Great staff, wonderful food, shuttle into town.
Day 5 Day trip enroute to Ischia. Ferry to Capri, 30 min. Luggage storage by the ferry terminal.
Head up to Anacapri on arrival. You teens will enjoy the chair lift up to Monte Solaro. There are some nice walks up here. Then walk back down to Capri town for your ferry to Ischia, 50 min.
4 nights Ischia. With 4 of you, and your wish for beaches, look here...
Edit. https://www.ischiareview.com/towns-of-ischia.html
https://www.ischiareview.com/ischia-thermal-spas.html
Day 9 Ferry, Ischia-Naples Molo Beverello 1hr.
Taxi to Napoli Centrale. There's a fixed rate fare to the station, with 4, it will be about the same fare as the Alibus. Train to Rome. Edit:
https://www.napoliunplugged.com/wp-content/uploads/2018/03/Tariffe_taxi_2017.pdf
4 nights Rome. If this is your first trip to Rome, I'd utilize a hotel.
Hope this helps.
The # of days for Ischia is not too much! There's more than enough to do on this beautiful island.