。
She mistook me for my younger sister.
Literal
She [topic-は] me [object-を] younger-sister [as-と] mistook.
The frame Xを Yと間違える ('mistake X for Y') uses を for the thing actually present and と for the thing it was wrongly identified as — exactly mirroring English 'mistake X for Y' but with positions swapped. 間違える ('to mistake, to confuse') is the transitive verb; the intransitive 間違う ('to be mistaken') exists too with overlapping uses. 妹 specifically means 'younger sister' — Japanese kinship terms always encode relative age (姉 'older sister' vs 妹 'younger sister,' 兄 'older brother' vs 弟 'younger brother').