She isn't his older sister — she's his mother.

Literal

She [topic-は] his [genitive-の] older-sister [is-not-ではなく], mother is.

~ではなく (or its less formal equivalent ~じゃなくて) is the negative copula in continuative form: 'is not X, (and) Y.' It links a denial of one alternative to an assertion of another in a single sentence — cleaner than splitting into two clauses. The formal ~ではなく contrasts with the casual ~じゃなくて. The polite です on the second clause keeps register consistent with everyday polite speech.