The Rainbow Princess.

Hope has an act in a traveling circus where she is "the rainbow princess" and performs a Hula dance. The owner of the circus pawns the girl off on Judge Daingerfield as his long-lost granddaughter. Hope goes to live with the judge, and to the horror of his upstanding family, insists on having the circus performers over as her guests. But the whole ruse, unbeknownst to her, is so that the circus owner's sons can rob the judge.