Be very careful with how you are describing (and counting) your days, eg - "we'll stay through Sunday." Are you flying home on Sunday, or Monday?
Start looking at specific dates for specific events. What date is your flight out (departing to home)? Most folks would want to spend their last night actually in their departure city (or at least pretty close to it), not hours away - to avoid the nail-biting "are we gonna make it?" if trying to travel any significant distance to reach the departure airport on the actual day of departure.
Lots of things can go wrong, and missing the flight home can bring painful expense. So, assuming you will travel to the city of your departure (or someplace pretty close) the night before you leave, how many extra "beach days" do you really have?
Ischia sounds lovely but you will expend a large part of a day getting there and most of another getting back. Ferries add more uncertainty when you absolutely gotta be somewhere after taking one. Unless you have plenty of slack in your schedule (or you are OK with high-risk choices), I'd stay on the mainland, and I'd choose my beach location very carefully (someplace not too far) with an eye towards being 110% sure you won't miss your flight home due to a flat tire, road construction, a train strike, etc.