Hi as A WDW veteran with a 4.5 yo and 1 yo, I don't think you will regret bringing it.
Here's why-
1. A stroller is indispensible at a crowded airport. It keeps the kids contained in one place and serves as a great place to stow all of your carry-ons. You can wheel it right to the gate and the attendants will check it for you. It will be waiting for you when you deplane.
2. If you are staying at a "mega" resort, the walk to the bus alone can be exhausting for kids your age. You can load up all of your gear the kids and your off to the bus.
3. We use ours when going to the pool, again, load it up and your off.
4. Disney strollers are not at all condusive to sleeping toddlers, IMHO they are only good for 5 plus year olds, whose parents don't even own strollers anymore and need a place for their older kids to rest. They are made out of hard molded plastic, which I assume get hot and sticky in the sun, and the canopies offer minimal sun protection.
5. Your kids ARE going to nap in the parks- they will be on sensory overload and might want to crash. My daughter was 2.5 on our first trip and was asleep at 9:30 am before we even made it to the end of Main Street in the MK. This is a child who doesn't nap, but still naps at WDW. My husband especially enjoy going to EPCOT for dinner, putting kids in the stroller and walking around looking at all of the grown up things. They are invariably asleep by 7:00, we stroll right out of the park before Illuminations and catch our bus/monorail before the mass exodus. Speaking of monorails, you can usually push your stroller right onto the handicap car if unused, without folding it up-Big plus!
6. The crowds at closing can be very scary, throngs of people heading to one exit. Again the stroller serves as a safe place for them and you won't have to worry about them getting lost or trampled (seriously). Also, the stroller return line gets long at opening and closing sometimes and the last thing you need is another line to stand in. While waiting for disney transportation thay will enjoy a soft comfortable place to sit.
7. It's much easier to find your own stroller in a crowded stroller parking area.
8. It's more economical to bring your own.
In closing, I think the pros far outweigh the cons, the only con I can think of, is that they are not super convenient to lug on and off buses. If you clean it out before the bus comes though, all you have to do is grab the kids and fold it. If you would like a recommendation--I have a Graco Duo rider, side-by-side-I call it my disney stroller. It turns on a dime, Is fairly light weight and is super easy to open and closes flat. It has 2 huge baskets for all of your stuff, plus anything you might pick-up on the way. It was less than $150 at Babies r us. If you subtract the $$ you would spend on rentals, that might be an option for you if you feel your current double is two bulky. Anyway---Hope this helps!
PS-Bring the car seat for the plane too.