If you would quiz your son's 14 year old friend just a bit, you probably will find out that he saw a picture on a calendar of "shipwreck Beach" -- a dramatic (and lprobably photoshopped) aerial view of a curved beach, blinding white, with cliff sides and a submerged "wreck". You should know that the beach is not sand, but white pebbles/rocks (true sand in the Med/Aegean is NOT white, but golden) ... and that the beach is never seen this way -- it's seen from crowded Excursion boats that pull up, hordes pour off, then return. Many people go to places based on what they thumb thru, on their I-phones. That's NOT how to plan a trip.
Also, why Hydra? Because of R Steves promotion? It's mainly promoted because it's a one-day trip for people who don't have time to see an island otherwise. It has a picturesque harbor, no cars, donkey carts to ride, and pistachio nuts to buy. The inland, you can walk around, lots of people have homes there, behind hi walls. Lovely views.
Why Kefalonia? Before beach weather, what attracts you to it?
You need to do MUCH more reading, very quickly becuse your itinerary is unrealistic, not to say impossible. Dellphi is a 3.5 hour drive, and should NOT be done in the evening, it ends in steep winding mountain raods. You cannot do Delphi in the AM, get to Meteora and do it in PM (another long drive, plus, in spring monasteries close at least by 2;30 - 3).
This whole thing is just not do-able. A do-able thing would be, upon landing, immediately get a domestic flight to an island -- Santorini, Naxos, Paros, you pick. The way you've planned, you start Day 2 with ambitious fast-fast sightseeing agenda, and with teenagers, jet-lagged, that just wont happen; you & I both know they won't be underway before 11. If you go first to an island, you wake up next AM in a beautiful place, low key, easy to explore etc. Then after 3 days, go to another island for 3-4 days, both Naxos and Paros have lots of hiking opportlunities, stuff to see & do. THEN back to Athens for One Night.
Nexd AM, Get car and go mid-day to Delphi, see it lin late afternoon, early AM next day, then off to Meteora for the night. See monasteries next AM, then in afternoon, Back toward Athens -- but you then could veer off and go over the Corinth Canal -- lots to do/see within a 2 hr drive -- some examples:
• NEMEA - an "Olympic style" restored Games venue... with stuning stadium where teens could race from ancient start-line ...
• MYCENAE or TIRYNS, ancient fort/castles • NAFPLIO - gorgeous old town with Huuuuge Fortress PALAMIDI in back, kids could climb its 999 steps • EPIDAURUS, a magical huge (15,000 seats!) ancient amphitheatre with perfect acoustics
Point is, lots to see & do in alternatives to beach going because, surprise, Spring break is NOT swim-season in Greece (unlike the US). And if you rethink the sequence, you'll spend less time in wearying & costly transit, more time enjoying adventures.