We’ve gone on NYE, Easter Sunday and other bonkers busy trips.
You know the drill already – rope drop is your friend as usual. We usually do not leave during the day when it’s that busy just because we don’t like fighting the crowd to leave and then get back in later (really only an issue for us at MK.) You have stroller nappers/resters so that is great.
When we need an afternoon reprieve on the busiest days at MK, we do things like Country Bears, HoP, Tiki Room, Philharmagic (although sometimes busy) Tom Sawyer Island, TTA, CoP, etc. At Epcot we tour the countries in WS during the busy afternoons. A good thing to do if the kids are resting. At AK, we do the FotLK or Nemo shows in the afternoon. DHS I don’t have a lot of suggestions other than get there early and use FP and you should be fine.