I agree about the pen and autograph books for DCs - you can buy them in park shops if you don't bring them with you.
We are used to carrying bags, but just took a small backpack that DH and I alternated carrying. We also had a bag with a spare outfit each in the car in the carpark daily.
Water bottles (full in the morning from apartment, and refilled from drink stations during the day). We also asked for glasses of water (free, iced), in addition to our occasional Coke/fizzy orange, at every meal. DD also loved going into all the various water sprays - and dried off again in minutes. Hydration is vital!
A pack of boiled sweets - in case energies flagged at times (DD has aspergers so we wanted to avoid hitting meltdown territory). A snackpack of raisins, bag of crisps and something like a snackpack of 2 oreos daily, emergency snacking as above (in fact, it was me who hit meltdown one day and needed them most). Some days we brought sandwiches or substantial picnic-y food, most days we got food in the parks - it depends on your budget and tastes.
Suncream. Cream for DH and I, solid stick for DD (hates cream).
Everyone wore their sunglasses.
Money, park tickets, keys, phones etc.
It was so hot that we didn't bother with ponchos - if we got wet, we dried quickly and there were usually plenty of places to duck into.
A couple of slightly cooler days and ones we were staying late, we put a cardigan for DD in the bag.
Pen daily, and park maps if we already had them for today's park(s). We used bring the guide book in the car but not into the parks.