I love old black and white movies, and this is a good one:

(1959) Aspiring actress Lora Meredith (Lana Turner) meets Annie Johnson (Juanita Moore) a homeless black woman at Coney Island and soon they share a tiny apartment. Each woman has an intolerable daughter, though Annie's little girl Sarah Jane (Karen Dicker and, later, Susan Kohner), is by far the worse. Neurotic and obnoxious, Sarah Jane doesn't like being black; since she's light-skinned (her father was practically white), she spends the rest of the film passing as white, much to her mother's heartache and shame. Lora, meanwhile, virtually ignores her own daughter (Terry Burnham and then Sandra Dee) in a single-minded quest for stardom. Legendary movie director Douglas Sirk's last American film.

http://www.imdb.com/title/tt0052918/