Over eight years, Dolores Jacobo earned her place as an integral member of an affluent Malibu, Calif., household, where her workplace is a six-bedroom, nine-bath beachfront home with a private movie theater. Hired to be the nanny of twin 3-month-olds, she stayed with the family after the girls started school. She transitioned from pushing strollers to shopping for groceries and ferrying the family's golden retrievers to grooming appointments. Her employers, she explains, "have busy lives" that include volunteering at school, going to the gym, visiting the chiropractor and getting various beauty treatments, like facials, manicures and pedicures. Later this month,...