It's true that there were a significant number of white (European) indentured servants/slaves in the Americas during the first centuries of colonization:

From Barbados to Virginia, colonists long preferred English or Irish indentured servants as their main source of field labor; during most of the seventeenth century they showed few scruples about reducing their less fortunate countrymen to a status little different from chattel slaves – a degradation that was being carried out in a more extreme and far more extensive way with respect to the peasantry in contemporary Russia. The prevalence and suffering of white slaves, serfs and indentured servants in the early modern period suggests that there was nothing inevitable about limiting plantation slavery to people of African origin.

reference

Between 50 and 67 percent of white immigrants to the American colonies, from the 1630s and American Revolution, had traveled under indenture.

Wikipedia article

However, by the 1900s white slavery really only persisted in the form of sexual trafficking of women, which ultimately led to the passing of the Mann Act in 1910. It's also likely that the idea of an organized slave trade at this time was hyperbolic:

While prostitution was widespread, contemporary studies by local vice commissions indicate that it was "overwhelmingly locally organized without any large business structure, and willingly engaged in by the prostitutes."

To claim that her father was a "slave" in the 1930s is a serious misappropriation of the term.