Kelly, I hope you can learn from experience of others, and avoid the pitfalls we can warn about ... factors having to do with crowds, heat, children, etc. The basics:
• DON'T Do ATHENS FIrst - I know it's tempting, u think that's the place to recover. NO. You'll be exhausted from long journey, and Athens will be big, noisy, confusing; the sights will pass in a blur. Recover on an Island, then come back refreshed. ALSO, in summer the Greeks leave for the weekend, so Athens will be quieter then. IF your arrival flight is in AM, you can proceed immediately to next step (see below). IF you have changes, & arrive at 4 pm or so, totally exhausted, I can recommend a nearby hotel ON a beach with a free shuttle... you can go there, have a dip, early meal & hit the sack, then go to an island early next day.
• ISLAND VISIT - (do this the 1st 2 days) You've timed this for Weekend: BAD idea. Athenians totally flood nearby islands on weekends.. less on weekdays. Hydra is constantly plugged by R Steves because it's convenient add-on to his totallly-mainland trips. However, be aware... NO taxis or vehicles available, almost no beaches... luxe accommodations have pvt. beaches or pools. I'd like you to consider AEGINA instead. It's a 1-hour ferry ride, 1/2 the time Hydra takes... and a conventional ferry w. open decks to sit on, a seascape adventure -- huge liners, schooners, tiny sailboats, gulls, shore views etc. (Do NOT take Hydrofoils - inside seats only no views). Find a hotel on a beach, taxi there on arrival, & just vedge for a day or so. Here's a great photo album showing a day-trip, and 2-night stay would be a great recovery time http://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/ Here's a place I have recommended - it's a cafe on the beach that just behind has a bldg with apts for families -- http://www.aeginagreece.com/aegina/pages/beaches/la_palma_marathonas_cafe_bar_restaurant.html
----- FERRY NOTE: the Conventional Ferry goes about 8:30 am then again @ noon. Last return conventional ferry is 6:15 pm. If these don't suit outbound you could take hydrofoil outbound, deck ferry back. Buy tix at any ticket agency... even at airport.
• ATHENS TIME -- Again as I said, busy Athen is somewhat better on weekend ... I hope hope hope you've been on internet to find lodgings! It is totally essential with 2 little ones to be CLOSE to landmarks... you need to be walking distance when 1 or both have meltdowns. This "tiny URL" of booking.com - http://tinyurl.com/heq6edp -- shows available places nearest to Acropoilis (click on MAP VIEW). Fortunately this agency now shows pvt apts, which are great for your bunch and often better price than hotels!.
• NAFPLIO - Your timing is better here... weekdays VERY busy in July but at least less than weekends. Old Town is a problem for family like y ours because almost no swim pools, and town beach & swim club has no accomm for kiddies. Nearby TOLO beach is not my Fave... a tacky package-holiday hive. A tiny beach nearby (Kastraki - also called Asine) is much better -- but v. hard to find accoms. Here's a great one if you get lucky -- https://www.booking.com/hotel/gr/porto-assini.html