Hi Jennifer,
Sounds like a great way to celebrate your mom's birthday! As for child care, several of the resorts have
Children's Activity Centers where you can bring your children ages 4-12 for an evening out. They provide games, movies, crafts and even dinner.
Teppen Edo in Epcot is quite fun if you like hibachi food? I would follow that up with a stroll to the Boardwalk and drinks at Jellyrolls, a dueling piano bar. Biergarten is also a fun dining experience in Epcot.
Would she be interested in character dining?
Cinderella's Happily Ever After Dinner at 1900 Park Fare in the Grand Floridian features characters from the classic movie. The Stepsisters are a riot!
Downtown Disney might be your best bet: House of Blues or Paradiso 37 are both great spots.
Then there's always Whispering Canyon Cafe in the Wilderness Lodge.
Keep in mind that even the "fancy" restaurants at Walt Disney World are not "stuffy". Dinner at California Grill to watch the fireworks, or an evening spent at Jiko are wonderful dining experiences.
Hope this helps. Have a magical vacation!