Peggy Mashke tends to 12 children for 12 hours a day at her home, so she was surprised to get a letter welcoming her to the United Auto Workers union. "I thought it was a joke," said Mashke, 50, of northern Michigan's Ogemaw County. "I work out of my home. I'm not an auto worker. How can I become a member of the UAW? I didn't get it." Willing or not, Mashke and 40,000 other at-home providers are members of a labor partnership that represents people across Michigan who watch children from low-income families. Two unions receive 1.15 percent of...