We have been lucky in that our Anaheim hotel has always let us check in early. One year we got there at 8.30am, and they still gave us the keys to the room even thought check in was at 3pm - they even invited us to go to the breakfast room and help ourselves to the buffet breakfast. I always email in advance and advise we will be arriving early due to the timing of our international flight (doesn't hurt to remind them you have just flown 14+ hours to get there) and they have been expected us with a room allocated.
This time we might not be so lucky, given we will be there in mid December. I expect the Hotel will be very full. As Iffam mentioned, most hotels will store your luggage for no cost, which will be my fall back position. But Iffam does raise a very valid point, and for some families, booking in that night before to guarantee you have a room when you arrive might be worth the piece of mind of knowing your family can have a rest when they arrive.
When we leave we check out at the regular time (although our hotel and I think a couple of others offer a late checkout for an additional fee), store our luggage at the hotel (no cost), go to Disneyland for the day, come back around 6pm to met our transport who takes us to LAX for 10.30pm flight.