It's because Yamato loves freedom, and hates what Kaido did to Wano. Yamato wants to be like Oden, because she wants to be free, like you said. Yamato's just a little mentally ill, since... well, her entire life has been horrible.
She'll get over the Oden thing as she explores the world, once she leaves Wano. She's already gotten a lot better about it, honestly.