Don't go all the way back to your room for naps. Just find dark and/or relaxing places in the parks. The baby centers work, but are boring for
mom.
How about the Hall of Presidents at MK? Also at the MK, the People Mover (aka Tomorrowland Transit Authority) is great for getting in an in park nap. Both of my boys have loved it. If you tell them as you board that you are hoping for a nap and want to ride multiple times if your child falls asleep, as long as there isn't a long line (and there hardly ever is), then you can just motion to them/say that you want to stay on as you approach the ride exit and they will let you ride again. Rode it five times in a row once!
The same is true for the Three Amigos boat ride in the Mexico building at Epcot. (At least the music isn't as annoying at "It's a Small World", even if the ride is much the same.)
And lock for rockers! Yes, they exist, you just have to look real hard. There is a blog out there somewhere on this topic.
And sometimes we just leave MK or Epcot and get on the resort monorail and just ride around a couple of times. Or ride the boat from Epcot to Hollywood Studios. Something about the motion seems to be nap inducing. Then head back into the park post nap. (But actually going to the room has never worked for us. Something setting foot on our resort property seems to induce a state of "wide awake" that just won't quit. I gave up after about the third try with each kid. Waste of everyone's time and energy. But I have some great photos from the pool area when we were supposed to be napping!
And I wouldn't worry too much about the "schedule" if I were you. Both mine were fine within a day of arriving back home. There is way, way too much stimulation at WDW for a wee one NOT to get off schedule. It is okay. Little ones tend to sleep really hard on the way home/next day and then just get right back in the groove.