We have 5 kids ( I had 5 babies in 9 years, 13 months a part, 3 years, 18 months apart and then 3years again).
We debated the double vs double and a single umbrella as needed. We never did take a single umbrella with us and ended up baby wearing often. I know many on these boards swear they could walk the park at 18 months just fine but I call bullsh*t. Most kids 5 and under need a break from walking, sun, crowds., etc. Kids tend to fall alot and we have some nasty road rash in WDW that might put an active 5 year old in a stroller for a bit. Your 5 year old can get a horrid blister and be out for a few hours. Kids can suddenly get sick in WDW, like our out of no where onset of Streap Throat and put a 6 year old in our stroller for a few days. But the most important reason I want my big kids in the stroller and babies on me is SAFETY! I have had a few expierinces in the hub around firework time and after Fantasmic where the push of the crowd has seperated my hand from holding my childs hand and that scared the crap out of both of us.
Generally speaking the baby is worn and the older kids sit in the stroller in and out of park and from one land to the next. So they hop in from Tommorrow Land to Froniter Land we then park stroller in Frontier Land and they walk between the attractions there.
Be open to wearing your older kids as well. A few years ago my 6 year old was fine walking around World Showcase and my 3 and 1.5 toddlers were napping in the strolller. Our daughter, 5, was DONE! I got out my wrap and did the russack (backpack like carry) while she got a little rest until we got to the American Adventure where she sat and wached the show. After that she was fine and we weren't listening to her bellyaching nor was the rest of Epcot and I got to walk off my School Bread
If you do plan to baby wear please don't use a Baby Bjorn, there is mountians of evideince that supports how bad they are for your babies bone structure. I love my Ergo as another option and just got one off of Craigs List for my SIL to use for $50.00. I love the ergo for babies and toddlers, over Mothers Day we were at the local Zoo and our baby was sleeping in the stroller and my 4 year old son fell and scraped his knee pretty bad. I carried him for about 30 mins on my back in the Ergo and we both were comfortable. He was then ready to finish walking after that.
I LOVE wraps but the Moby is way to hot for you and baby in WDW. I found an awesome lady on etsy.com that makes mesh wraps that are very breathable and strong! That mesh wrap is what I used when I carried my 5 year old on my back in Epcot.
You didn't mention what kind of stroller you have. I have had 6 different styles of double strollers and a few you could squeeze 3 kids into. If you have the tandum style like a Graco duo glide you can recline the back seat to the lowest postion and seat your lightest kid there with a next lightest in front, sitting between that childs legs. The heavist would go in the front seat. Some side by side have big enough baskets for a kid to sit it too, I know both sound crazy and its not ideal or a long term soultion but it will get you down Main Street faster. I currently have and LOVE is the Britax B Ready that can be a single or double with the 2nd jump seat that sits underneath. I love it becauase my 4 year old is pretty good at walking rarely wants to be in a stroller, so we don't alwasy need a double. Our Mothers DayTrip to the Zoo DH forgot to put it in the trunk and if my 4 year old wouldn't have fallend we wouldn't have needed it (thus me wearing him for a bit).
Anyway Good Luck like others have said you can always rent one and there were some decent strollers in gift shops for about 25.00 that would work as well.
Have a Magical Vacation!