It is the shame of Spain. An estimated 300,000 babies — the Niños Robados — were snatched from their mothers at birth and placed with new families.

ZARAGOZA, SPAIN—In November 1974, Luisa Fernanda Marin Valenzuela stood in a doorway at a medical clinic. A male nurse held one arm and a nun held the other. About 36 hours earlier, she had given birth to a baby boy. Far across the room, she could see a tiny baby’s naked body on a table. They told her it was her dead son.

She wanted to get closer, to hold him, to cover his cold skin, perhaps even whisper his chosen name, Antonio. But the nun and nurse refused to let Luisa, who was wracked with grief, move closer to the child. Instead, they led her away.