You are talking about the former Kingdom of Sikkim. It is not quite where you thought it might be. It is located in the Himalayas, bordering Tibet to its north, Nepal to its west, Bhutan to its east and India to its south. Sikkim became the 22nd state of India in 1975, and ceased to be an independent kingdom.
The lady you refer to is Hope Cooke of the USA. She was married in March of 1963,[as his second wife] to The Chogyal Palden Thongdup, the King of Sikkim.
After the loss of his kingdom, the former king's health declined and in the early 1980's he died a broken man. His Queen, left Sikkim and is now known again as Miss Hope Cooke, of NYC. She is the author of her own autobiography, which I understand is quite fascinating.
BTW,I love trivia games..............bring them on! LOL