I checked the 1999 edition of The National Directory of Children, Youth & Families Services and found this :
Wyoming Children's Society, POB 105, 716 Randall Ave, Cheyenne WY 82003; phone 800-584-9384.
If your mother was in the orphanage in 1930, she would be listed therein in the federal census of 1930. Ancestry.com prepared a surname index to that census for the benefit of its subscribers. I have seen queries on message boards in New York State that indicate difficulty in finding the proper enumeration district for some censuses. It may be a good idea to seek a volunteer to look up the census for you, someone with experience in that type of research.
Maybe you'll find the right person on the message board for the county in which Cheyenne is located :http://boards.ancestry.com/mbexec?htx=board&r=an&p=l...