Spirited Away AU/influence? Where Elsa was banished/sent away to live in the enchanted forest with the trolls. Anna arrives and tries to find her way out after some misunderstandings as Elsa tries to help her. Elsa can't remember her own name but for some reason she can remember Anna's.
Oooooooh. Maybe once Elsa struck Anna accidentally, the trolls offered to keep her, teach her to control her powers? Took Anna’s and Elsa’s memories? Both not knowing who “Elsa” is? With Anna the same reasoning from the movie; with Elsa to sort of, free her from her earthly trappings so she can focus on her magic. She grows up with the trolls and Kristoff as her only family, learns how to control her magic and is happy... mostly. Aside from a hollow longing that’s been there ever since she can remember.
And then when Anna’s 15 and her parents die, she goes to the enchanted forest to find a way to bring them back. Cue getting lost, almost getting eaten by wolves, and stumbling upon the lair of some sinister fae who says they can bring her parents back but she has to stay there forever? She gets scared and runs and runs into the valley of the living rock, which she was looking for in the first place. The first person she meets is Elsa, and they feel like they know one another. The trolls had promised to give Elsa her memories back when she could control her powers, but they never did - some because they loved her too much and didn’t want her to leave, some because they thought giving her her memories back would make her lose control, or get really angry with the trolls.
Grand Pabbie tells Anna that there’s no way they can bring her parents back to life, that Kristoff would guide her back home because the forest is dangerous. Anna thinks they’re lying (they are being shifty because of Elsa) and ditches Kristoff to find her way back to the fae who promised her they could return her parents to the living. Elsa, who was following behind Kristoff and Anna, runs to save her, brings her back to the trolls who are like “well we can’t restore your parents but we can give you back your family” and return Anna and Elsa’s memories about being sisters.
(Bonus if they kissed before getting their memories back heheh)