This thread creates what I considere the RS Forum's greatest flaw -- when one clicks to answer, all the previous posts disappear -- including VITAL infiormation.. so one must open another window. (Rick, fix this problem!)
I see you are travelling in HOT weather, with a tiny baby AND elderly parents... a recipe for disaster if you et over-ambitious. When I add up the time-commitments in Turkey (3 or 5) I come up with a maximum of 8 days or so for Greece, Including to/from Samos and to/from Samos to another island... with a newborn, a 2 year old and parent in the heat. Groan. We visited the N Aegean successfully but we were 4 healthy adults, going off-season in lovely weather, and did much advance "homework":
Have you checked out Samos? the best-known beach - Pythagorios - is a busy busy "package holiday" favorite for UK & Europe ... other beaches are either so - so.... or far far away from any points of interest. The port of Vathy has much of interest & I've stayed there 2x -- but only has small mediocre beaches -- a huge challenge for finding accommodations for your group.
As for visiting other islands -- another huge challenge ... we mianaged it, one May, by staying in Vathy & being willing to take ferries either at 7 am or midnight both ways -- to visit Chios and Patmos... and then went on to Naxos (but that ferry connection disappeared 15 years ago)O. Now even to nearby islands only a few ferries a week in July.. And ery llimited publilc transportation (unlike Samos which does have a bus network). And at this late date, accommodations are heavily booked. I highly recommend that instead, you think about 2 locations on Samos.
In sum, I think you risk a nightmarish situation unless you get VERY professional help... and are willing to spend what it takes, not only for lodging but perhaps car rental as well (and think about car-seat rentals! that puts you into a 3-row seat van situation). I'm getting a headache.
I recommend you immediately contact 3 Athens-based agencies that are accustomed to working entirely online with newcomers to Greece; they all have excellent reviews. Fantasy Travel, Dolphin-Hellas, and Aegean Thesaurus. You need email all of them at once, same t ext, -- you'll have to give fairly exact dates -- be specific ab out lodging needs (double beds/single/ cots/Kitchen?) ... indicate need for walking distance to restaturants, beaches etc, and rough est of budget range per night. Then see which answer fastest, & compare prices. It's your best hope.