With a three year old, you will have to take breaks.
What worked best with our DS was getting to the parks way before opening (better to wait 40 minutes one time, than for every ride!). Just bring his breakfast or something to play with or color- the CM's are really great with interacting with the kids, too.Let him walk around with one adult, while the other one holds your place in line. Don't line up behind other people if there are turnstiles wth no one waiting.
We would take a break after lunch, go for a quick swim and lay down for a nap (just turn on toon disney, if he resists-works every time). We have lwasy foudnt eh best way to ge our Ds in bed is to get in ourselves. We usually do fall asleep, too!
Then we would get dressed and head out for the evening- usually a character meal or Epcot.
A word about Epcot- we got our DS used to doing Epcot in the evenings. He seems more agreeable t this time of day to doing the slower paced attractions. Spacehip Earth, Living Seas , the Land (Food Rocks and Circle of Life), Ice Station Cool and Journey into your imagination. Then we would head around the WS , starting in Canada, since we were on that side of future world. At this point he was content to sit in his stroller and maybe color at the kid cot stations, if we stopped. This has worked without a hitch for SIX trips!!!! Going to the other parks in the mornings and doing things he liked, let us get to enjoy Epcot without him even realizing what we were doing! Our Ds is 5 and half now and always talks about Epcot and how much he loves it!
Have a great time!!!!