LOS ANGELES — WHEN we talk about immigration to America, we tell a hopeful story about courage and sacrifice. But that story obscures the fact that, especially for the poor, immigration is often a traumatizing event, one that tears families apart.

Consider the experience of one family, originally from Honduras. In 1989, Lourdes Pineda was the single mother of a 5-year-old boy and a 7-year-old girl. She sold tortillas, plantains and used clothes door to door, but barely earned enough to feed her children, and feared not being able to send them to school past the sixth grade. So she made the painful decision to leave them behind in Honduras, and found work in the United States as a nanny, taking care of other people’s children.

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