Roger:
Thank you for responding and for looking for info on my behalf. The names for the parents, according to the limited documentation I have -- Eleanor's death certificate and handwritten family notes -- are John Arnold and Eleanor Fitzsimmons. I take from the info that they were not married. The situation appears to be a family tradition, as at least one of Eleanor's daughters appears to have had children without benefit of marriage. My sense of Eleanor's own marriage is that it was an unhappy one. Her husband was a low-wage laborer in the western Kentucky coal mines, and I think he may have been a heavy drinker and possibly in trouble with the courts from time to time. That could have influenced their daughters' opinions about marriage. Maybe Eleanor herself did not marry because of family situations in her own childhood.
The research challenge is tougher because the only one of Eleanor's grandchildren who appears to have produced children is a grandson who died young in a construction accident. His wife remarried and moved with her new husband and her children to New Orleans. I have not been able to trace those descendants.
It had not occurred to me to flip the surnames to see what comes up, but it's worth trying.
I did autosomal DNA testing via Ancestry.com and mtDNA testing through familytree.com at least 8 years ago. I uploaded the autosomal to GEDmatch.com about 5 years ago. I haven't mined the DNA results and matches as efficiently as I could have. I am on the verge of hiring a professional to do that.
Thanks again for responding. I'm determined to learn more about Eleanor.
Fran