Will go back to read more thoroughly, but we just went to WDW with a 6yo and 21 month old, and our 6 yo has been to WDW frequently at the 2-3 ish age. Our kids, even now, are on the same schedule at home - overnight 8p-6a, and #2 naps from 1-3.
Trips when #1 was a toddler were rough, but we almost always took a resort break because #1 never napped except in a darkened room in her bed (or toddler bed, or pnp). But it had to be in a "bed" in a room. ARGH. But, we did it, even that year we stayed offsite and had a car. I would not recommend this - but on that 1 trip, we had 6 adults to 1 kid in an offsite condo, and 3 cars, so we were able to go back and forth fairly easily and meetup with the adults after nap.
#2 was 21 months when we were there in August, and she's a really good stroller napper. We generally still did midday breaks because WDW is just very tiring, it was super hot, and everyone appreciated a chance to wind down in the middle of the day.
As you can see from my signature, we stayed deluxe, but went to all the parks.
Generally what we did was:
let kids wake up when they wake up (6:30, at best). Slight hustle to park for rope drop or pre park open ADR. Enjoy parks until ~11am. Pick up lunch to eat at resort.
11-12 park to resort (includes leaving park, transportation, etc).
12-1 or 1:30 pick up lunch if we hadn't picked it up on the way out of the park; eat in room
1:30-3:30/4: NAP (everyone naps, if we can make it happen)
*sometimes we'd have to wake the kids, and sometimes there would be massive meltdown.
4-5(ish): return travel to a park (had PHs) or dinner. If dinner was in a park, sometimes there was time to do a ride or something right after dinner.
Back in room by 7:30/8, bedtime.
When we only had 1 kid, we would *on occasion* stay up later, or sometimes push it until 9 or even 10. We almost always had a meltdown on the way out of the park, but we might only have 1 or 2 late nights in a 1-week trip, which was manageable. If the kid fell asleep on the bus on the way back, it wasn't so horrible for bedtime since they were so tired by then we'd be able to get them to bed pretty easily.
With 2 kids, we've been a little more structured about the schedule, and since we bought DVC, don't always go back into the parks after nap since we don't feel as pressured to do everything on each trip. On the most recent trip, we only went back to MK after naps at the GF, and to EP after naps at BCV. One day (during the VGF part of our trip), we used FPs at MK, then went to AK, and pushed nap/lunch to later (#2 had a meltdown on the bus from AK-->VGF - apologies to everyone on that bus!!!), and just did pool and easy dinner at the resort after nap. (and one day we walked to/from BCV and HS and #2 fell asleep in the stroller before we left HS, and she ended up sleeping for 1.5 hours in the stroller! So we just went with that and had lots of fun pool time after she woke up.)
my point - stroller naps are great if you can get them to happen, but they're not that restful. And you may end up with a meltdown anyway. You know your kids and your family's energy level - I'm a big fan of the midday break because I HATE the heat, and I grew up going to WDW during summer vacations (thunderstorms and heat anyway), and we'd nap at WDW even though we never napped at home. And then my sister and I got to stay up for all the late night activities too.
Now with kids, we just do early bedtimes and it's fine.
