If you are staying on Disney property you can use the DME and they will claim your luggage for you. the DME is a free bus service. With small kids this would be a great options as long as your flight arrives before 10:00 p.m Disney will collect your luggage. The luggage service closes at 10:00 p.m
Then when you leave you can check in for your flight with RAC desk. They are open 5:00 a.m to 1:00 p.m They will print your boarding pass and take your luggage to the airport and the next time you see your luggage will be at your final destination. You must check in with them no later than 3 hours prior to your flight time. Or before they close at 1:00 p.m