。
She mistook my older brother for me.
Literal
She [topic-は] my older-brother [object-を] me [as-と] mistook.
Xを Yと間違える ('mistake X for Y') is a stable pattern using と as the quotative/equational marker — 'mistook 「brother」 as 「me」.' 兄 is the in-group form for one's own older brother, the same kinship-by-relative-age system that splits 姉/妹 for sisters. The implication that the brother and the speaker resemble each other adds a touch of color — Japanese siblings being mistaken for each other is a common conversational scenario, especially given the cultural fascination with sibling resemblance. The pattern Xを Yと間違える also extends beyond people: 砂糖を塩と間違える ('mistake sugar for salt') is identical structurally.