Hi Steve, I have added the 1940, 1950 censuses to Rosetta's profile page. She was residing in the home of her grandfather, Edward Setser. Then, I added her birth registration in 1931. Only her mother is listed on that - Ethel Setser. So it appears that Rosetta was illegitimate. If you haven't already, I suggest that you take a DNA test. For an autosomal test take an Ancestry test. Their data base is much larger than the others. Then, if you get some clues from that, take a Y-DNA test and that has to be from FamilyTreeDNA as they are the only company that tests Y and mtChrondrial.
I would research the mother, Ethel, and her parents and find as many sources as you can and post those to their profiles. It helps to know as much as possible about the family. Do the same for Rosetta's siblings and her aunts and uncles. You will develop family groups and you can see on the census records the neighbors and see who witnessed marriages and witnessed deeds and other records. It all will help.