Don't worry about the rain - it's usually no more than a brief interruption to your day and can actually be a welcome relief, because it lowers the temp by anywhere from 5-15 degrees. Bring ponchos and forget the umbrellas; ponchos are lighter and work not only in rain but on water rides, too.
Instead, worry about the HEAT. August in WDW is not just "hot and humid", it can be downright dangerous for those from the north. I notice that OP is from Toronto - well, if you're not accustomed to the ravages of 90-plus-degree heat coupled with high humidity, you're in for a shock. And you may not be adequately prepared for it.
Firstly, make sure you and your family carry water bottles at all times and drink LOTS of water. Dehydration will sap your energy and make you cranky and tired long before you even start to feel thirsty. Cold water is best, of course, since it will cool you as well as re-hydrate you, but drinking even warm water will re-hydrate you, which is a plus. Hint: you can get cups of ice free from any restaurant or counter-service eatery if your water bottles get warm. Don't drink a lot of soda-pop; the sugar will give you tummy aches. Instead, stick with plain water, or if you get a little dehydrated, seek out Powerade, which is sold at plenty of places in the parks and is a sports drink designed to replenish fluids and electrolytes. I also like the taste better than Gatorade, as Powerade has less sodium and less of a salty taste.
Second, take a bottle of sunscreen into the park with you and re-apply at least once during the day. Depending on how waterproof your sunscreen is, you might need to re-apply multiple times as your sweat or water from rides washes it off. Nothing ruins a vacation faster than a health problem, and sunburn is one of the most uncomfortable. Don't forget the backs of your legs when wearing shorts, the top of your head if you have thin hair, and especially the tops of your feet if you wear any kind of open shoes.
Third, make sure to pack light-colored, loose-fitting clothes for the whole trip. Baggie shorts and shirts with lots of room for air to flow through them, made of light-weight, breathable materials, will help your body's natural heat to escape. And lighter colors don't heat up as much in the sun; white or khaki are best, black or dark blue are the worst. Dark colored clothes in the Florida sun will heat up like a solar panel, making you feel the heat far more.
And lastly, plan your days with lots of rest stops. Meals and bathroom breaks, indoor attractions and shows, and even snack and drink breaks (remember, water and Powerade!) can be used to give you a respite from the heat, humidity, and sun without making you feel like you're wasting precious vacation time. Mid-day breaks to return to your hotel for a nap and a refreshing swim, or even a cool shower and a change of clothes, are quite common, especially among those with small children.
The rain won't hurt you, or your vacation, significantly. But the heat can hurt you, and requires a lot more preparation than the rain.
Stay cool, and have fun!
I just can't decide how many of rain ponchos I need from the dollar store.
Storms can be brief to lasting several hrs. If it rains for awhile people with kids tend to leave, that means more rides, quicker, if you don't mind getting wet running between rides.
