We haven’t done a double stroller, but that being said, we think two single strollers is the way to go. We’ve done trips with them at 2.5 and 4 (they’re 20 months apart), 3.5 and 5, and 4 and 5 yr 8 mo., and brought 2 single strollers each time.
We find it to be much more versatile than what it seems a double stroller would be (and from observing others at the park, I’d stand by this). You can walk next to each other, or you can switch to single-file when it’s crowded or if in a rush (need to make an ADR or Fastpass), or even split up a bit to make your way through crowds. You also have the option to split up completely at times, especially if you’re taking the older one on rides the younger is too small for (our 4yo is very small for her age, she couldn’t even ride 7 Dwarfs when we went for her 4th b’day in April, so we did a lot of splitting up to take her to rides she could do when riding bigger rides with him).
Also, I think it seems easier to fold up two smaller strollers for the buses/boats (we stayed at Wilderness this last time and rode the smaller boats to Magic Kingdom) than a double stroller. Additionally, since you’re staying close to a couple parks, you may decide if you’re going in for a shorter time or just going somewhere to eat, you could decide to leave one of the strollers behind based on how things are going.
Just be aware, one of the biggest issues we’ve had with the two strollers is actually them fighting over which stroller, or more commonly, over who was pushing which kid (“I want Mommy to push meeee!”).
We’ve brought our own strollers each time - they’re free to bring on the plane and they can be nice to have in the airports. We brought our good Britax stroller each time. The first two times we brought a cheap umbrella stroller. That was nice because when it folded up, we could actually hang the curved handles over the handlebar of the Britax, so it was great for parking them in crowded stroller parking areas. That got kind of beat up though and was a bit small for our son, so this is what we bought for this past trip:
https://smile.amazon.com/gp/product/B017ERMTUK/ref=oh_aui_search_detailpage?ie=UTF8&th=1 We got one in a damaged box through the
Amazon Warehouse deals, so only paid $42 for it, which was worth it. It worked okay for both kids size-wise and still folded relatively small. I saw the suggestion elsewhere to, rather than
renting strollers, buy a cheap one(s) and leave it there - still cheaper than renting them. Obviously we weren’t doing that with our good one, and we’d rather just bring them back. We’ve really only used them for Disney anyway now for a while.