Heheheh, you want readers of the message board to choose between your unresolved bits of evidence?
While you could very well write a research 'note' or a more obvious 'comment' concerning what you have found so far, it appears to me that you need more facts.
Did your great grandparents have other children? If so, how is the mother's name entered in death or birth or (with luck) marriage records?
Are they shown as a couple in Census enumerations? If so, exactly how are their names given?
What records do you have concerning your great-grandmother? How exactly was her name given in each of them?
Could Esther's father be a man with the same name as your great-grandfather, not the same person?
Have you been to the local court records to look for a divorce record or possible paternity case?
Have you looked at surviving newspapers for announcement of birth and/or death of Esther? Are there obituaries for each of your great-grandparents that might list surviving children as well as one who died young? Have you looked for obituaries for each of their children that might list surviving siblings and a sister who died young?
Is the cemetery a large incorporated cemetery that might have burial records? Was Esther's a church funeral, and if so are there surviving church burial records? Could there be surviving funeral home records?
These are just some of the possibilities that can give you further clues about the identities of Esther, of her mother, and might confirm that your great-grandmother was her mother, or point in a different direction.
Bear in mind that records can have mistakes. In the death record of one of my distant cousins, you can see the sequence of questions asked by whoever was filling out the form:
1) Who was his father? Where was he born?
2) Who was his mother? Where was she born?
The informant's answer for #2 was the name of the mother of #1, rather than the mother of the decedent. The "his" in the question was ambiguous, and the informant probably was peeved at all the questions anyway, in addition to the stress surrounding the death.