Where the child looked white and the mom was black, in the 1930's I thought the movie was called invitation of life

Imitation of Life

Imitation of Life is a 1959 American film !959...
In 1947, Lora Meredith (Lana Turner), a struggling white widow with aspirations of becoming a famous Broadway actress, loses track of her young daughter Susie at the beach (portrayed as a child by Terry Burnham), and requests the help of a stranger named Steve Archer (John Gavin) to help her find the girl. Susie is found and looked after by Annie Johnson (Juanita Moore), a black divorcée with a daughter, Sarah Jane (portrayed as a child by Karin ****er), who is about Susie's age and, unlike her mother, is so light-skinned that she can pass for white, which she does with fierce zeal and fervor. In return for her kindness, Lora takes Annie in temporarily. Despite the fact that Lora cannot afford a nanny, Annie persuades Lora to let her stay and take care of Susie, so that Lora can pursue an acting career.