We live in the Caribbean and took the kids to Disney when they were nearly 5 and 2.5 - they loved it (there was a big group of us in Florida for a wedding).
We did Magic Kingdom and Animal Kingdom. We were there last week of August and it was MUCH quieter because the US schools go back before then.
Obviously it's despicably hot in August but you just dress accordingly and carry lots of water. Lots of places are kept water sprayed some you can cool off, it's all well catered to provide comfort where possible. We're used to the heat and humidity so it didn't really phase us as much.
In hindsight Animal Kingdom was probably not the best option for a park because of the long distances between exhibits (lots of walking), but Magic Kingdom was amazing. We went early doors (9am), did a bunch of rides and exhibits until midday, came home for lunch/nap because the heavens opened and there was a huge thunderstorm, returned for 3pm and stayed until the night fireworks. It was a brilliant day/night and the kids were well rested.
I just took night clothes to change kids into and then drove home and put them straight to bed.
We hired a big house at Reunion resort and it's about 10 min drive from the parks.
I'd recommend doing the rides/activities you most want to do first, and then the rest of the day you can relax and just enjoy whatever comes your way. Take a stroller (we ordered on Amazon and had one delivered to the rental house before we arrived), and take a lot of snacks to keep the kids occupied if you're having to queue for something.
Also use the Disney app to book your appointment for any of the Mickey Meet & Greets.