We always go in the summer months because the kids are out of school and it gets REALLY hot in July and August so we have learned a few things every year to keep cool. I suggest that you take a break during the hottest part of the day and go back to the room and nap...just get out of the heat and the sun. If you get up early, your family will need the rest and then go back in the evening. Your kids are little so they might not be able to stay out as late as we do but I'm sure you'll want to see the fireworks, parades, etc. We have taken the mister fans in the past but last year I found Misty Mates at Walgreens and bought two. The mist is very fine so it lasts quite awile and then we just refilled it at a water fountain or a sink. All 5 of us have our own personal mini fan and we walk into the parks for the day with one cold water bottle and one frozen one. We also found those bandanas the have the gel pebbles in them that expand when you soak them in water. My husband didn't want to wear his but me and the kids wore ours around our necks and they felt nice when it got to hot. And last but not least....the one thing that I found I couldn't leave the room without was a fan I purchased in China, Epcot. It is a simple fan that unfolds and is very pretty and very cheap but well constructed. It moved alot of air and kept all of us cool. (My husband even used it because it worked so well.) Last year we bought a few more so the girls could have their own and we used them everywhere because they fold up nice and small.
Have a great trip and stay cool.... however you decide to do it!! We are going at the end of June this year so we will have our "survival kit" with us again this year!!