奥様の

your wife’s

→ 奥様
phrase Uncommon #19,189
your wife’s 奥様 is a polite or respectful term for someone’s wife, and の marks possession or association. The exact English wording depends on context.
JA: 奥様のお部屋はこちらです。
EN: Your wife’s room is this way.

すべて処分して奥様のものです奥様は私です

Dispose of everything. It belongs to the lady of the house. I am the lady of the house.

— レベッカ (1940)

奥様のレベッカは美人だった溺れて亡くなったの

Your wife Rebecca was beautiful. She drowned and passed away.

— レベッカ (1940)

奥様のお帰りを寝ずにお待ちしたものです

I used to stay up waiting for your wife to come home.

— レベッカ (1940)

奥様の旧姓は何ですか。

What was your wife's maiden name?

奥様のお部屋でした

It was the lady’s room.

— レベッカ (1940)