Hi Crystal!
It sounds like you're starting to plan a wonderful Disney trip! Thanks for stopping by and asking the panel a question!
The months of June and August have two main things in common: Summer weather and school vacation. Both of these months will have pretty hot weather, and typically, are more crowded than September. BUT, this isn't necessarily a bad thing. We've visited in August and particularly enjoyed the fact that the park hours are usually longer, and that we could enjoy the parks after dark when the weather cools off. The hot months are also a ton of fun at the resort pools and at the water parks. Be sure to pack some rain ponchos, as Florida weather is notorious for a rain shower in the afternoon (just a quick shower, then things clear up again!).
Late August and September have the benefits of lower crowds as kids across the country typically head back to school. To go along with this, Disney often offers great values. This year there is a Free Dining
promotion which is hugely popular and a great money saver for many people. Park hours are a bit shorter than summer time, but the lower crowds compensate for this. Weather is still great for pool and water parks.
Personally, given your kids' ages, I'd take advantage of the ability to go in September before they start school. This way you can enjoy the lower crowds and great deals without feeling back about missing school days.
Hope this helps! Have a great trip!