Hi, Tracey! I know how disappointing it is not to be able to get the dining reservations you want! We often take last minute trips, and by the time we actually get the ball rolling, we are usually dining at whatever restaurants still have room!
There are other ways to visit the princesses! If you have exhausted the possibility of dining at Cinderella's Royal Table, Restaurant Akershus, and 1900 Park Fare at the Grand Floridian, you will still see some of your favorite princesses around the theme park, waiting to sign autographs and have their pictures taken! At the Magic Kingdom, Ariel has her own place - Ariel's Grotto - where she appears in her mermaid form to greet princesses just like your little girl. Also at the Magic Kingdom - at Toon Town - you will sometimes find the princesses at the Toon Town Hall of Fame Greeting room. Belle appears in the rose garden at Cinderella Castle for Story Time. You can check your park guide for times during your visit.
You will also see princesses in various spots through the theme parks doing meet and greets. We've seen Aurora (Sleeping Beauty), Jasmine, Snow White, and Belle all through EPCOT on various occasions. They usually appear in the World Showcase.
Don't worry about not getting those dining reservations. Your little girl will see them in shows, parades, and quite possibly in personal meet and greets throughout the parks!