Also, if there are any other suggestions you have in general for Athens and Santorini I would love to hear them. I would like to be able to leave Athens early morning on Day 3 so that we can have almost a full day on our first island. We would like to see as much as we can without feeling like we are running around from island to island the whole time.
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.