I'm confused. Are the kids toddlers or 5 and 6? That's a world of difference to me. Also, is the airfare booked yet? If so, what are the actual flight times?
I would be willing to do a day at DL with a 5 and 6 year old. If it's really two toddlers coming from the east coast, then I agree they will likely be asleep before you get to see much.
If your flights aren't booked, I'd fly into LAX late at night, and take a shuttle or Uber or whatever and stay at GCV on rented points. That direct entrance is amazing. I don't think we'd stay at DL again and not stay there. We've stayed at local hotels and a Dolphin Cove in the past, and they were fine, but Grand Californian is awesome. You'll want to go straight to Radiator Springs Racers or straight to the FP machine to get FPs for RSR, as that is the most popular ride. It's really amazing. Carsland is so immersive. It just feels like you are actually in Radiator Springs. Definitely get hoppers and go back and forth between DCA and DL as much as you like. I'd make sure to get back to DCA in time to see World of Color.
For that night, you could either do a second night at GCV and then Uber back to the airport bright and early or go to the airport late at night and stay at the Hilton. Either choice would be good, so it pretty much comes down to personal preference.
When is your trip? We'll have to compare notes, as we are going to Hawaii in May, and I will be taking a 5 and 11 year old. I am curious to hear how your kids do on the flight. We're considering doing an overnight stopover in LA or SF. We talked about doing a day at DL, but I don't think we'll be able to fit it into our schedule. We'll probably do SF instead and take BART to one of the Starwoods in the city and spend the day in SF, as it's one of our favorite places.