I'm sorry to hear about your mother's passing, and the sad details concerning her birth. A birth certificate is the record of a child's birth. If someone misrepresents the truth on the birth record, there is no correct record of who the child's father actually was. Unless a contemporary of the child's mother is available to question about who the aboriginal father might be, there is no way to know.
DNA testing can help narrow the field once someone has narrowed it down to a few candidates. However, one cannot do DNA testing on every aboriginal family in the area hoping to find a near match for the woman's children and grandchildren.
I know this isn't what you wanted to hear, but sometimes it isn't possible to know all one wants to about one's heritage when along the way there are no correct records.