Hi Diana!
Welcome to the Disney Parks Moms Panel, and 'Hello' to a fellow Texan!
Disney's Magical Express is such an awesome perk to staying at a Disney Resort Hotel. I love not having to look up a map of a new city or worry about driving a rental car in a strange place.
Disney's Magical Express does pick guests up from Orlando International Airport 24 hours a day. Only the magical luggage pick-up and delivery portion of this service has a time cut off. This service does require that you and your party check-in for and then board your motorcoach to your resort hotel as your bags cannot travel without you, so your fly-in day must match your check-in day as there isn't an option to store your bags overnight. Technically the Disney Airport Cast Members are looking for yellow tags on specific flights. And because things do happen with air travel, Cast Members do also try to keep an eye out for all yellow tags as they come off the luggage carousels. However, if your arrival time is after the nightly cut off time for luggage pick up (10:00 P.M.), the Cast Members miss one or all of your bags, or you haven't checked-in for your Magical Express journey by the luggage cut-off time on Saturday night, your bags will be sent to the airline baggage office where you will have to retrieve them the next day.
Since you'll have to collect your luggage anyway with the way your trip is currently set up, it might be worth it to try to add a night at either your or another
Disney Resort Hotel when you get in on Saturday. If you end up staying at another Disney Resort Hotel, there is a complimentary luggage transfer service between Disney Resort Hotels that you can use on Sunday.
Something else that you can do to save a bit of time is
Online Resort Check-In. For your Sunday date especially, estimate your "arrival time" based on when you're aiming to board Disney's Magical Express. This should help your family get into a room earlier in the day.
I hope this helped to plan your upcoming Disney Days, Diana, and We'll See You Real Soon!
~Kristen