As a Mom of 4 also I get the panic in what do I need...but in truth not much! I strongly recommend you take a stroller and gate check it. This way you have what I call a portable locker!
For Flight::::::
-As for a bag I carry a crossbody purse that fits wallet, camera/phone, gum, small pack of kleenex, passports.
-My hubby carried a backpack filled with 1 diaper for every 2 hours we will not see our luggage and 2 spare, a small pack of wipes, small snacks, a water bottle we buy after we go through security, sippy cup, a few toys for smallest, an extra outfit for non potty trained kids in a big Ziploc baggie, kids Tylenol and adult Tylenol and gravol. A magazine for him and a book for me and headphones if your planes have tv.
-Older Kids each carried a backpack with stuff to do on the plane, a few snacks and their neck pillows
In the parks::::
we took our stroller and like I said used it as a portable locker. All 6 of us had our rolled up hoodies in the underneath basket, a small blanket (great for shading and spot saving), small medicine bag of Tylenol (adult and kids), gravol and bandaids, I also threw in the baggie with a change of clothes for those not potty trained, 1 diaper for every 3 hours you plan to be away from the parks, small pack of wipes, snacks and everyones waterbottle/sippycup. I also attached a few toys to the sunshade of the stroller. Never had any problems with theft on any of our 3 trips.
I carried my crossbody bag with camera, gum, sucking candy, Kleenex, small pen and paper and the gazillion maps my kids collected

, wallet, 1 diaper and small baggie of wipes.
Hubby carried his wallet.
Kids carried nothing.
Have a magical time!