Personally, I would have a secret plan that I just suggest when everyone gets up. Know the least crowded park and say that's what you feel like doing. Then they can take or leave it. And then do that again when you get to the park, like: "Oh, look! There's a 1:00 Nemo showing. Let's grab Everest fastpasses and go see Nemo." Then they can take or leave it. If they leave it, so be it.
If you get there at 11:00 you'll need to use Fastpasses wisely. But the only ride you wouldn't be able to get on potentially would be Toy Story Mania. It usually, even at slower times, will be out of Fastpasses by 11:00 to noon and has a 60-90 minute line.
If this were my trip, I would be taking my Nintendo DS & some paperback novels in my backpack. Then if the step-children wanted to stand in line 60 minutes I would find a shady spot, buy a Dole Whip or other lovely snack and people watch & entertain myself, cause I don't like really long lines. It's just a different touring style, not better nor worse than the rope drop plan. You just have to change your mind set that it isn't about the rides. It's about the ambiance.
You will be there at a slower time, though, so if you get there at 11:00 & stay until the parks close, you might be surprised at how many rides you can still get on.