Am I trying to do too much?

You should stick with Greece. You don't have enough time for the Naples area. Maybe add the Naufplio area in Greece. In 2008, we were able to go to another town near Naufplio and do a snorkeling trip.

I think Greece and Italy are way, way too big and complex to do in a single trip, unless you have a long, long time (many more weeks than you do) and/or you only want a quick sniff of each and won't be sad to be "so close...yet so far" to all the amazing things each has to offer. It's your trip, but...I'd pick one, not both.

Don't think of Greece as one small country (or even one large country). Unless you confine yourself to the mainland, Greece is more like about half a dozen small countries, and it will probably take much longer than you expect to get around within any of them, let alone between them. Crete is essentially a whole 'nother country, so are the various island groups. Many a Greece vacation plan has come up against hard truths about the time it takes to move around (welcome to the club - I'm still trying to make things work!).

Italy has fewer islands to contend with, but even sticking to the mainland, it's so big and (like Greece) has so many appealing "must see" places that are far-flung and strung out across long distances, even traveling efficiently (by train where you can), for most folks it requires multiple trips to even scratch the surface. It takes time to move between locations.

On a "14-15 day family vacation" you will be hard-pressed to knock out more than just a few of your "must see" locations in either country. Count your usable days carefully and honestly, and remember you burn at least half of a day when changing locations (and when you throw in Greek ferries, the time in transit skyrockets).

As they say, if you have to ask, then yes, you probably are. 2-3 nights is not near enough for Naples and Sorrento, plus Capri.

I agree with the previous poster, stick with Greece. While a day in Athens to acclimate has great value after a trans-Atlantic flight, maybe plan the bulk of Athens for the end, if you will fly home from there. Getting from the islands to catch an International flight is risky.

You will spend too much time traveling for the time you have.

This would be my suggestion.

Fly to Santorini and start there. Spend 3 nights.
Ferry to Crete and spend 8-9 nights.
Fly to Athens and spend 3 nights. Fly home from Athens.

On our first trip to Greece, we traveled with our young adult children. We started in Santorini, they were totally amazed. We spent 3 nights like I am recommending. We did the hike from Fira to Oia like you are planning.

A few years later we went to Crete. We spent 11 days there and it was not enough. There are beaches, hiking, and historical sites. Chania feels like you are in Venice because it was conquered by the Venetians so you can have a bit of Italy that way.

I would go to Santorini before Crete because while Santorini is stunning, you will love Crete. I would return to Crete in a heart beat.

It is most efficient to visit Athens at the end.

Since the essentials have already been said, I'll just add that BethFL's suggestion seems the most appropriate, even if you'll spend far too much time traveling from one place to another.

While enjoying the Greek food and wines of Santorini is a great idea, you'll quickly realize that cycling in Athens is an activity for courageous kamikazes. You can remove this activity from your wishlist.

To me, they are two different trips. However, I would consider the stopover in Naples only if you are flying from so far away that breaking it up helps in some way. Is it a month with flights from Santorini to Naples?
Capri is a full day thing--I don't think you can do all of that in one day.

We haven't been to Greece yet, we go in October and have 16 nights there.

We have been to Sorrento and the Naples area though, and stayed for a full week, and we needed every minute.

We did a day trip to Capri, and we needed the entire day, there is no way you could appreciate it combined with Positano and the Amalfi Coast, that is at least a separate day.

As the others have said, add much more time or make it two trips.

We travel from Australia so it is super long and super expensive, from my limited knowledge of coming from the US, it seems much more affordable, so just do Italy next year.

Also, visit the New Acropolis Museum in Athens.