Did her daughter or her son live in the country same years ago?
Did her daughter live in the country оr in the town same years ago?
Did her daughter live in the country same or ten years ago ?
Это альтернативные вопросы к разным членам предложения.
А вот общий вопрос:
Did her daughter live in the country same years ago? Yes, she did.
Did her son live in the country same years ago? No, he didn,t.