What's the Matter with Helen? (1971)

Set in the 1930s, Helen and Adelle are two women whose sons commit a gruesome murder. After their conviction, they move to Hollywood, change their names and open a dance school for girls. Adelle is looking for a good life, and when one of the parents of her students who is wealthy takes a liking to her, she thinks she's got it made. Helen thinks that someone who blames them for what their sons did is stalking them. But Adelle thinks it's all in her mind.