True, however, the sister doesn't know the backstory; and since Doyeon went out of her way not to fill her it just looks like a bad situation with severe repercussions for her family. As such, lil sis appears to be acting out of protective instinct for her family. We, the audience, know what the real deal is but she does not. Lastly, I get the bit of resentment you touched on since it appears that Doyeon may be naturally gifted in many things (yes, innuendo implied) and what sibling doesn't get jealous over stuff like that? Add the fact that Doyeon is adopted just heightens the already very petty sibling rivalry.
While I get what your saying, I, however, can't fault the sister for acting on the situation as she knows it to be, since she was not privy to all the relevant details.