If you are still seeking info about this, you may be interested to know that Crittenton Hospital is a large general hospital in the Detroit Metropolitan Area. It is now located in Rochester, Michigan, a northeast suburb of Detroit, but the original location was in the inner city.
The Home for Unwed Mothers was just a part of the institution. I also was born there, but back in the 1930's. My parents were legally married. Our family doctor worked out of that hospital. My mother said that the young pregnant women worked around the hospital, doing cleaning and other jobs; she saw them while she was there for her Cesearean operation. I think if you contact the hospital, they might be able to give you some leads to the info you want.