Near the beginning of Part 2, DG affectionately calls her father, "Popsicle" (derived from the more common "pop" or "papa"). This is the same name by which Glinda the Good Witch addresses her father in the salutation of a letter home early in "Wicked," a Broadway musical also based on the Wizard of Oz.
During the dream sequence, DG is asked if she's been having dreams again, and she says, "Yeah, in Technicolor." The Wizard of Oz (1939) movie was one of the iconic pioneers of the infant Technicolor process.
The girls' tutor's name is Toto. This name comes from the Oz stories where Toto was Dorothy's pet dog. This is also shown by the fact that Toto can turn into a dog.