Hi, Benjamin!
Congratulations on your upcoming trip to Walt Disney World! I'm really happy to hear that you've made your dining reservations in advance of your arrival. No worries at all about the shows you're planning to see at Disney's Hollywood Studios and Disney's Animal Kingdom Theme Park! The three shows are all offered multiple times per day. You'll want to check the Times Guide when you arrive at each theme park to confirm the show times (as they are subject to change).
I checked the show schedule for you and on Sunday, January 27th,
Beauty and the Beast - Live on Stage is offered at 11:45 AM, 1:00 PM, 3:00 PM, 4:15 PM and 5:30 PM.
Festival of the Lion King has the following show times on Monday, January 28th:10:30 AM, 11:30 AM, 12:30 PM, 1:30 PM, 2:30 PM and 3:30 PM.
Finding Nemo - The Musical is presented at 11:00 AM, 12:00 PM, 1:00 PM, 3:00 PM and 5:00 PM on Thursday, January 31st.
I know you'll enjoy your dining experiences and all the wonderful entertainment you have planned during your trip! Please don't hesitate to come back to visit us here on the Moms Panel with any last-minute questions before you leave for your magical vacation.