Is it also best to get private/smaller ferries for the island hopping?
Private ferries, small or large, don't exist, and there's no way to travel by sea in the Greek islands other than taking the standard ferries, which are basically the buses of the islands. Of course, unless you charter a private boat with a skipper and crew for an organized tour, which costs thousands of euros per person and follows a pre-set itinerary.
While Santorini and its unique landscapes are pretty much unmissable, chances are Mykonos will disappoint you and won't be a good fit for your mother, it's arguably the worst destination you could choose. Even though it's world-famous ,it's one of the most expensive destinations in the Mediterranean and a major stop for massive cruise ships. The island is tailored for people who know exactly why they're there: primarily a global party hotspot for a young, wealthy, late-night crowd, as shown in this video:
https://youtu.be/dMpaksY4sTE](https://youtu.be/dMpaksY4sTE
That said, you might even end up on local television: :-)
https://youtu.be/WCsdnAs3qIs
Instead, head to more authentic islands. There are nearly 20 others in the Cyclades, all featuring whitewashed houses, blue domes, and sandy beaches if that's the kind of environment you're looking for in the Greek islands.
Although not mandatory, it is preferable to save Athens for the end of your trip. It would be better, for instance, to catch a connecting flight to Santorini upon arrival in Athens, spend 3 days there, then take a ferry to another island before finally returning to Athens for your final 3-day stay.
