Julie gives wise counsel. I've learned about Aspergers traveling (a friend of mine ran bus tours in Greece for Asperger teens). The one thing she said was MOST important to comfort level (and these were teens, high-functioning) was not too much change, and having predictable routine. Your schedule does not seem to allow for that -- especially with choices listed & going at Height of High Season. Even w. lodgings "away from the towns" -- in order to do fun stuff, you must cope w. crowds. AND (very importantly) transferring from one island to another will involve lots of luggage, standing on crowded ferry piers, rushing with crowds into ferries and scrambling for seating, and ditto on disembarkng. BTW, boarding a Blue Star Ferry at the Santorini pier in high season is a mob experience I would not wish on anyone. It's taxing enough in May or September. If you DO visit & leave Santorini by ferry I recommend the new Large CHAMPION Jets, all-reserv seats. Of course, they are more expensive than the Conventional ferry ... but you can perhaps save by skipping Mykonos. So you want to cut down the number of destinations on your wish list.
ALso, It appears you're trying to plan a long trip with special requirements, and budget limits, before doing adequate research. Browsing Airbnb for nice apartments doesnt tell what u need to know about each area. U need detailed & CANDID guidebooks, NOT just the web. Many websites motive is maximum visitors, so they omit drawbacks & realities. A good guidebook must be more truthful and candid or it loses readership. Hi the library for ROUGH GUIDE to GREECE -- also if you can find it, a back copy of GREEK ISLAND HOPPING. Very detailed & truth-telling about travel in the crowded high season. Among the Choices you list that reveal information shortfall:
• MYKONOS & SANTORINI - in High Season hugely expensive, very crowded. In Mykonos, even if far from a beach, when u DO hit the beach, a sunbed & umbrella can cost €20+ (as opposed to €5-7 on other islands). And in the afternoon do your kids like to drink & dance on tables? As for Santorini, no decent beaches -- all about the view; and pool hotels in July are €€€.
• You speak of flying between islands, but there is virtually no such plane service. There is ONE airline, Sky Express, that does go between a FEW islands (i.e. Crete to Rhodes). but they have tiny planes, you are only allowed a 15-lb or so carry-on, and a checked bag of the kind u will be bringing would cost €25-50 EACH if indeed the airline even allowed u to check them. so you see, you need to know what is possible... and that needs reliable research. About Zakynthos, it's nowhere near any of the others and in high season has an overload of package-tourism, to boot (they are the ones who call it Zante; the greeks hate that UK nickname).
• CRETE - you chose Rethymnon for a long stay for the purpose of "chill time" to recharge. Rethymnon is a major crete city, its Old Town is much smaller than Chania's Old town (and narrow streets get absolutely choked in hi season). It does have a loooong beach stretching East for a mile or so from town center. However this beach is lined with large-ish convention-type hotels, and I don't know if it's the refreshing, laidback atmosphere you envision. Have u googled any Rethymnon scenes? If you want relaxtion on the North Shore of Crete, I can suggest a very moderate-price FAMILY accommodation Just outside of Chania with a lovely pool that is a block or 2 from a nice beach, and NOT in the middle of a row of noisy holiday homes.. it has 1 BR apts (with liv room sleep-sofas), w. kitchenettes for self-catering, and right at the door is the local bus to Chania in 15 minutes http://www.lefka-apartments.gr
• NAXOS and ANTIPAROS are ideal for your family ... and both offer day excursions to other places.