Does the telling of the story constitute "fair use?" What legal rights
does the "teller" have to tell the story,
This analysis misses a key point. A story about you is not copyrighted unless you committed the story to writing or a recording and someone reproduced the way that you told the story and not just the facts involved in it.
If the story isn't copyrighted, then the issue of "fair use" which is a defense to a claim of copyright, doesn't come up. Anybody can tell the story without the permission of the person that the story is about, so long as a false and defamatory account of what happens is not told.
There doesn't appear to be any claim here that the person telling the story did so in a way that made false statements about the subject of the story that harmed the reputation of the subject of the story.
The fact that the story was used to advance political ends that the person who was the subject of the story disagreed with, or was used in a way that made a point that was politically misleading is irrelevant. Political speech is particularly immune to legal claims under the First Amendment, even if there was a colorable legal claim here, which there really isn't.
what legal rights does the "subject" have to keep it out of the
spotlight, given that she is not a public figure?
Assuming that the person telling the story does not have a particularized duty of confidentiality to the person the story is about, no rights at all. Their lawyer or psychotherapists or priest isn't allowed to do that. But anyone else is free to put someone in the spotlight and to name names when doing so.
Public figure status has nothing to do with it. There is no generalized right to privacy or to be kept out of the spotlight in U.S. law.