We just returned on Sunday and we took breaks every day. In fact, DS (7), actually asked for breaks about 2:00 each day when the sun was getting very hot. We arrived at each park at opening, rode lots of rides without waiting because we were there early, then got back into the car, which was parked close because we were there early, and went back to our hotel, which was a 10 minute drive. DD (3) and son swam, didn't sleep, but recharged their batteries. We ate an early dinner off-site, sometimes in the room because we reserved a fridge. The heat really made them not want to eat much, so we all survived on wraps, granola bars, cereal and milk and fruit. Saved lots of $$ too.
One hint for the return to the park. Sometimes we would be directed to a parking spot way at the back of the park. Tell the attendant you're meeting friends at your original and much closer parking area and when it's time to leave, you'll be very close to your car. We always got a great spot upon returning to the parks around 5-6 becuase lots of families that didn't choose to take the break were leaving or park-hopping. Also, if you take the break and have a hopper option on the ticket, you can go to another park for evening shows, fireworks, etc. We were only there for 4 full days, and took breaks each day, and we crammed everything in with no meltdowns. Maybe try a day with a break and see if it helps keep everyone happy. ps: get squirt bottles with the fan for the heat. and get each kid their own if you can so they won't fight about them. When you get into a hot car at mid-day, it was the only thing that kept them from complaining. Good luck and enjoy!