Well, I'm glad you had an easy time with yours. My umbrella strollers weigh less than 7 lbs and I have never seen a double that was lighter than that. My double was a Maclaren and was a heavy, unmanageable beast. I wouldn't take mine around my neighborhood for a walk, much less Disney World! I sold it for $10 just to be rid of the thing.
I guess this just goes to show that a putting thought into the things you buy is important. I assume the OP would do that.
I can think of at least half a dozen scenarios where I'd take strollers through stores at Disney. For instance, you can wait out a rain shower while keeping both your child and the stroller dry by ducking into a shop and browsing. I it's crowded on the main thoroughfare, you can get out of the park by going through the stores. If your older child is riding a ride, the younger one is tired, and it's hot outside, you can browse in an air-conditioned store while waiting. We've always found Epcot/World Showcase a great place to explore when a child is sleeping in a stroller, but you can't do that if you won't take the stroller inside the stores/exhibits.
I would think that not everyone tours WDW like you do. I should think you should assume the same. Just because you would do something, certainly doesn't mean others will too
Umbrella strollers fly through stores because they have to be accessible to wheelchairs so the aisles are wide enough. Side-by-side doubles are too wide to get through and back/front doubles and sit-and-stands are so long that they don't corner well enough, making it so much more likely that you're going to clip the corner of a display and knock something over, or not be able to navigate at all inside. They're also much harder to handle because you have the weight of two children in there, instead of just one. (I'm picturing my kids and that could be almost 70 lbs of child for the ages that the OP listed.)
Just some things to think about.
Ummm, ok. In your stroller research have you used each and every side by said stroller? Because my Combi didn't have these issues. But in your stroller expertise, you already know that.
Much like the person complaining about the wheelchair user above, get your ankle clipped by someone who is having problems steering one of those land yachts and you'll hate them quickly enough. Same for the person using the double stroller who cuts people off because they don't turn easily (or the person using it as a battering ram to get through a crowd, which is not to say that you did that)! Or the person taking up an entire bus row with their stroller while you and your kids stand. Or the person who lets their 20 lb behemoth fall over onto you or your kids on a bus ride.
It's just my opinion that, at Disney, those giant strollers are sot often a pain in the rear for the owners and a menace for the other guests. If you don't *need* one, I wouldn't do it.
Again, don't assume everyone uses the exact same stroller as you. Step outside your box for minute. I certainly know how to push a stroller. I would bet most moms do.