If you click this picture to enlarge it, you'll see that the sister with the white veil is certainly Laura Hesch (if she needed glasses, she didn't wear 'em for her wedding photo in 1933).
Sue contacted the Franciscan Sisters in Little Falls, and the answer came yesterday. In part:
"The two women with veils in the photo: The one wearing the white veil is a Novice and the next step for her would be First Profession or First Vows where she would receive her black veil.
The woman standing next to the gentleman is a "Postulant" who would not have the title of "Sister" as of yet"......
"Loretta Anna" Hesch
Parents: John & Catherine Hesch; Birth November 10, 1909;
Entered: November 10, 1926 (she was 17);
Reception: August 12, 1927;
First Profession: August 12, 1929"....
"Sr. Whilomina received her "Black Veil" at her First Profession on August 12, 1929".
I think the picture was taken BEFORE the First Profession ceremony that day in August, 1929.
A special thank you to Judi Welle, Director of Archives, Franciscan Sisters of Little Falls!