After six years working in the laundry of a Miami hotel, Julia Rivera was thrilled when her union tapped her to become a full-time union organizer.

But her excitement soon turned to outrage.

Ms. Rivera said her supervisors at Unite Here, the hotel and restaurant workers’ union, repeatedly pressed her to reveal highly personal information, getting her to divulge that her father had sexually abused her.

Later, she said, her supervisors ordered her to recount her tale of abuse again and again to workers they were trying to unionize at Tampa International Airport, convinced that Ms. Rivera’s story would move them, making them more likely to join the union.

“I was scared not to do what they said,” said Ms. Rivera, adding that she resented being pressured to disclose intimate information and then speak about it in public. “To me, it was sick. It was horrible.”