「小姑のような人」は英語で someone that's like a sister-in-law といいます。
小姑は英語で sister-in-law です。
のような人=someone that's like
例文:
職場に小姑のような細かい口うるさい人がいます。
At work there's an annoying person that's like a sister-in-law.
There's someone at work that's like a sister-in-law. She's annoying and nags a lot.