I think it all depends on your touring style.
If you are planning on hitting the parks at rope drop and stay until night, your kids will probably need some rest, but if you have a sit down meal and plenty of rest stops, it might be doable.
If you do one side of magic kingdom one day and the other side another day, you cut walking by half, so that might be easier on your kids legs.
Disney Hollywood Studios is a lot easier on the feet, since it has a lot of sit down shows and is smaller, this one you can definetly do with only the 3 year old´s stroller.
Animal Kingdom covers a very large área, but has less attractions, so it can be done in less hours.
And probably for Epcot you will need the stroller.
You could also rent a doublé stroller like the City Mini GT, that has higher weight limits and sit the 3 year old there and the older kids can take turns. And if you have an ergo or something, the older kids could ride at night, coming out of the parks and you could carry the 3 year old.
I wouldn´t want to push a sit n stand stroller with 3 kids, in my experience they aren´t easly to push, on the other hand, either the city mini or the Maclaren strollers are a lot easier to push with heavy kids.