We were just planning out the bag situation last night for our trip starting Saturday. I am a total bag lady so this was a very important planning step for me.
What we plan to do is pack a small duffel with everything possible that might be needed, but probably won't (extra diapers, extra extra change of clothes, baby Motrin, first aid kit, extra sippy cups etc.) and put it in a locker every park day. I have a large waterproof bag we plan to put 8-10 diapers, a change of clothes and some wipes in to keep in the stroller, a smaller one we plan to put the touring plan and maps in (in case of rain), and then one backpack with the cameras, wallets, cell phones, tickets, sunglass cases etc. DH might insist on a camera bag and backpack, but if so he can carry it.
I happened to have the waterproof bag set for watersports, but large Ziplocs would also work and I considered them.
That sounds like an awful lot of bags. Also, the lockers are near the entrance so if you're in Fantasyland and decide you need something, its a hike.
Here's what I had in my slightly larger than I would normally carry on a regular full day out diaper bag:
6-8 diapers
travel size thing of wipes
A few disposable bibs, changing pads, and table topper place mats
A full change of clothes in there (rolled, in a ziploc with the air quished out - great tip!) + an extra bottom (pants or shorts) just in case.
At night I would throw PJ's in there too (because my son would ALWAYS fall asleep on the bus. That way when we got back, he would just go to bed and take a bath in the morning)
A few snacks (small snack size zip loc of cheerios or the individual baggies of goldfish)
Travel size magna doodle (keep him occupied while in line or at restaurant)
Video Camera
Digital Camera
Sunscreen and lip balm
Antibacterial hand gel
A few bandaids and the smallest bottle of baby tylenol I could find
Rain Ponchos (the ones that are folded really small from the dollar store) only if the weather report required them.
We also had a small softside cooler to carry bottles of water/juice/milk/fruit and things that needed to stay cold. That stayed in the bottom of the stroller. Tickets, money, photopass, ID, etc was in a lanyard around my neck.
Our first trip I had a huge bag with so much "just in case" stuff, it was impossible to find anything I really needed when I needed it. And even though you are in the park, it's not like you're on an island like Survivor and won't have access to the rest of the world.