I can't imagine dragging all that stuff around all day!
A fanny pack per peson should be plenty. Every person big enough to walk should have a fanny pack to tote his own stuff. You need your room key, ticket, money (but not your whole wallet), a small snack, and a camera. Wear your sunglasses.
As for flashlights, I bought two TINY penlights -- the kind that take two
AAA batteries -- for my daughters. They're the kind that clip onto the zipper pull of a fanny pack, so they take up zero space inside the pack. They can use these for just a moment in totally dark rides without disturbing other people. It's nice for little kids.
Things to leave in the room:
Sunscreen -- it lasts six hours -- put it on before you get to the park. You can get a small stick of sunscreen if you're particularly fair skinned -- it's the size of a fat chapstick.
Pins and autograph books. Who cares about those things anyway?
Guide books. Write down your game plan for the day on a note card and bring that along. Do write down your priority seating confirmation numbers -- just in case.
Water bottles and drinks. Use a water fountain -- it's easier than carrying a drink all day long.
Exceptions:
If it's definately going to rain hard, I'd carry a small backpack for the whole family's raincoats; this would take the place of the fanny pack for the day, and my husband and I would take turns carrying it. If rain is a maybe thing, just go into the shops and wait it out.
If you have a small child, you'll need more stuff -- but you'll also have a stroller.