poor little rich girl

(idiomatic) An unhappy young woman from a wealthy background.

Example: 2003, Svetlana Boym, Ninochka (page 172)
  One is a cheerful and spunky orphan, another is a poor little rich girl. (The poor little rich girl speaks with a British accent. The spunky orphan wears her baseball cap backwards, so you don't have a problem figuring out who's who.)
2006, Dorothy Stephens, Kwa Heri Means Goodbye: Memories of Kenya 1957-1959 (page 96)
  Not all of the girls in my Guide Company were poor little rich girls. Mandy was a poor little poor girl, a mousy waif who lived out Thika Road, far from Muthaiga.
2010, Michelle L. Levigne, Have Yourself a Faerie Little Christmas
  So, are you a poor little rich girl, slumming it and hiding from boyfriends who only want your trust fund instead of you?