You’d have to check the schedule for your specific dates but I think Santorini then Milos then Paros then Naxos and Athens would probably be the best order. 3 days in each sounds great. Or a small tweak: 2 days in Milos and then 4 days in Santorini (splitting time between 2 of the 4 caldera towns) or even 4 days in Paros (splitting time between Naousa and Parikia).
I liked the price and the hotel is perfect for kids. I stayed in a bungalow close to the pools and that room was great! You can park your vehicle close to your room so you don’t need to walk like 2 blocks to get to your car. The hotel offers great facilities for the kids, but if you are planning to walk around Las Vegas strip this is not a good location.
You seem to have your heart set on Zakynthos but I have to say it’s not a good use of time for a sort-of overrated payoff. Your time is much better spent (in my opinion) seeing another Greek island in the cyclades (maybe taking a ferry to Naxos or Paros sitting outside on the deck drinking a bottle of wine) rather than taking a bus and connecting flights. Zakynthos and Santorini/Mykonos are on opposite sides of the country and the only way from one to the other is by flying (or some combination of bus and ferry). So, my recommendation is to consider spending those Zakynthos days in Naxos, Paros, Milos, or some other Cycladic island.
Other factors, such as surface transport facilities and onward connections, will also affect the relative appeal of different airports and some long distance flights may need to operate from the one with the longest runway. For example, LaGuardia Airport is the preferred airport for most of Manhattan due to its proximity, while long-distance routes must use John F. Kennedy International Airport's longer runways.
Since airline reservation requests are often made by city-pair (such as "show me flights from Chicago to Düsseldorf"), an airline that can codeshare with another airline for a variety of routes might be able to be listed as indeed offering a Chicago–Düsseldorf flight. The passenger is advised however, that airline no. 1 operates the flight from say Chicago to Amsterdam, and airline no. 2 operates the continuing flight (on a different airplane, sometimes from another terminal) to Düsseldorf. Thus the primary rationale for code sharing is to expand one's service offerings in city-pair terms to increase sales.