I have only spent 24 hours or so in Naples (1 hotel night), and we slept 5 nights in Sorrento because it is such a good base for daytrips in the immediate area. Naples is loaded with history and with art. But it is a gritty city that has a ... what's in it for me (?) ... culture, based on decades of neglect by the northern-oriented national government. Sorrento is a postwar, purpose-built, reinforced-concrete resort town, built on a cliff with essential no beaches.
That sounds like a slam on both places, but I am only trying to make sure that you have some information for further study. We liked both of them fine. Both places have a high tourism load, anyway, and are worth visiting. I grew up in a city, and happen to like them. It is fair to say that Naples is not at all "like Rome." But Sorrento is also unlike both of them, in the way that (poor comparison) Orlando is not "like Miami".
I try to avoid important religious holidays in observant countries. American school vacations are not observed in Europe. I don't have a 13-year old child, but it sounds like you need to give a lot more consideration of how to engage him, based on his interests and emotions. Have you checked April climate? Any point in watching "That Hamilton Woman" or "The Borgias"?
https://www.accuweather.com/en/it/naples/212466/april-weather/212466
Sorrento books up six months in advance, most of the year. Pompeii was on my must-see list since my second year in college. How would he feel about that? Any interest in the Royal Palace in Caserta? I think one or two movies were filmed there. (?) I don't think it's on any 13-year old's list, but the Farnese Marbles in the Naples Archaeology Museum are life-changing. I think his ages prohibits (?) his admission to the Pompeii brothel frescoes in the same museum.