You should start with a copy of your father's birth certificate.
Michael D. Douglas
Born: 20 Aug 1952, Breckinridge, Wilkin, mN
Source: Douglas Family tree, www.ancestry.com
You can order a copy from the Minnesota Office Vital Records.
His father's name might be on his birth certificate.
If it's not on his birth certificate and Glee received support from his father, there will be court records. The Wilkin County Court Administration has court records starting in 1884.
If she didn't receive support, then you might want to consider a DNA test. I don't know much about it, but the DNA Detectives, www.thednadetectives.com
has a good web site that explains it. Successful Searching!