IMO, the key is being flexible depending on what your plans are. We go as either 2 of us, or 4. But it's only myself or myself and my wife carrying a bag. We don't make the kids carry anything.
I also bring 3 different bags for myself- a backpack with 2 large side water holders, and large hip/sling pack with 2 large side holders and a small fanny pack that has 1 smaller. Wife has either a backpack or a small fannypack. The large side holders can fit a 32 ounce nalgene. The smaller ones a standard store bought water bottle of 16 ounces or so. We bring Nalgene bottles- that are not insulated, so would be the first thing to drink on longer days. We also freeze some plastic waters as others have said. We also have 2 of those steel lined water bottles that we can put ice in and be cold for 12 hours.
All that said- every day is different. If we are just going for a quick 2 hours- I take the small fanny- and one regular refrigerated water. On long days- we have a backpack with a nalgene on one side, steel on the other and a few frozens in the pack. However- any time we grab a pretzel or an ice cream etc- we each get a free water- and down it- and extra we'll dump in our waters. It keeps stuff cold, and us hydrated. However, we never go without any water, because I don't want to "have to" wait in line for a water if I really need it. Flexibility is my most important aspect to water at the parks- and frankly- without water and being hydrated, all the parks are frustrating...