I wouldn't worry about traveling in July. Yes, it is summer so it will be hot, but the Polynesian has not just 1, but 2 pools to help cool off. There are also plenty of indoor attractions that will help cool you down during the heat of the day. And I think with the age range of children, the main pool will be blast with the volcano slide, zero-entry, splash area, and music played under water. Also, you can watch the fireworks while swimming!
Because of our sons' school schedule, we are typically limited to visiting WDW during peak times. By using fast-passes and taking advantage of Extra Magic Hours in the morning, we've always felt like we were able to accomplish all we hoped to without having to wait in any long lines. If your family can do the same, I think you will be just as fortunate. If your family doesn't like to get up and get going early in the morning, just travel opposite of the AM Extra Magic Hours to avoid entering an already crowded park.
And as for the Polynesian, it is incredible -- particularly for the transportation. We like the building Tokelau because it is so close to the bus stop, right next to the quiet pool, a quick walk to the Ticket and Transportation Center to catch the monorail to Epcot, a short walk to the Great Ceremonial House to catch the monorail to the Magic Kingdom or to go to the main pool, and a short walk to the boat launch to go to the Magic Kingdom. We've never experienced long waits or crowds to catch any of the various forms of transportation.
I also have to point out a great secret about Tokelau. While the rooms have garden-views, guests simply have to exit the room/building and turn. The Magic Kingdom can easily be seen from most of the patios!