A directory issued in 1922 has two entries :
1) St. Mary's Hospital, no address, in Green Bay. Conducted by Sisters of Misericorde.
2) St. Mary's Mothers' and Infants' Home, 403 S. Webster Ave., same nuns. It is probably akin to Marian Hall who was listed in 1966. Additional text can be found in any library that purchased "Adoption Agencies, Orphanages and Maternity Homes : An Historical Directory."
The address of the motherhouse of the order of nuns can be sought in the latest edition of the "Official Catholic Directory." I do not imply that the nuns are anxious to share the records with you, but you seem to be a courageous person.
Good luck from Reg Niles