Hi Michelle! The Tower of Terror is going to be a great race! I can't wait!
There is a child-care service called "Kids Nite Out". They are not owned by Disney, but they do contract with them. Here is a link to information about
child care services at Walt Disney World Resort. Some resorts do offer some programs for children, but I don't think their hours will work with the race schedule. The "Kids Nite Out" company is available 24 hours a day, 7 days a week.
I have never used the service but plan on using them when my husband and I are there for the Wine and Dine half marathon. I did, however, poll the 70+ panelists on the Disney Moms Panel and there were more than a dozen who have used the "Kids Nite Out" company, and they all gave glowing reviews. Some of them even use them on every trip for a "date night". I didn't want to recommend them until I had some personal recommendations from trusted friends.
I hope this helps! Have a great time with your friend, and let me know if I can help you in any other way!