According to Birnbaum's WDW Without Kids, the following restaurants are open 24H on property:
Captain Cook's Snack Company at the Poly
Food and Fun Center at Contemporary
Gasparilla Grill & Games at GF
Tubbi's at Dolphin
Offsite:
Crumpet's Cafe at Grosvenor
Watercress Pastry Shop at Wyndham
Sandwiches and Pizza are available from room service at almost all resorts until 11pm. Most deluxe resorts, including AKL, have 24H room service. They can pretty much get you anything on the hotel restaurant's menu. Wilderness Lodge and Poly offer room service until Midnight only.
This is just a guess, but chances are the ESPN club will be open late, as well as most of the restaurants at the Marketplace (Fulton's, Rain Forest, etc.)
Your mom is going to flip if she can't eat at Captain Jack's the first night you get there!
