I have an alternate for Frozen... Arendelle exists in the Avatar world, and signed a non-aggression pact with the Fire Nation, as had the Kingdom of the Southern Isles. When Elsa's powers are realized, rather than keep her locked up in the castle, the king and queen send Elsa and Anna away to the Southern Water Tribe for training, where she meets Katara and Sokka who recently lost their mother.

Thus begins an alternate history for the G'Aang.