It is difficult when you cannot choose when to go, we are restricted to August.
June/July will be very hot, July is probably (sorry) the worst month of the year to go...it really is extremely hot, we think August is bad but last year July was worse.
You are always going to get a lot of rain, however, these tend to be afternoon or evening thunderstorms rather than persistent (uk type) rain.
You can usually tell as the day progresses , although the storms can often come and go very very quickly.
I think if you go June/July you just have to take your days easy, try and get to the parks in the morning and in the evening to avoid the worst of the heat, July can also be pretty crowded too...the big advantage though is the parks are open later, so you can take advantage of enjoying your stay there at cooler times of the day.
Sorry, if it's all doom and gloom - a holiday in the summer will be marvellous for you - you just have to be aware of the high temperatures.