- Ayn Rand can't be in apposition of my mother as there's no comma setting Ayn Rand off from my daughter
- Similarly, Ayn Rand and my daughter are not in apposition
- my daughter and my mother are mutually exclusive
This is described in more detail here:
https://en.wikipedia.org/wiki/Serial_comma#Ambiguity
> "To my mother, Ayn Rand, and my daughter"
Adding the Oxford comma creates ambiguity between my mother and Ayn Rand, unless the speaker is Ayn Rand's daughter.
Semantic disambiguation also imposes a higher cognitive load on the reader -- sometimes that's the point (high-brow writin'). But you should consider the poor reader. After all, you want to be read and understood.
That's not possible so we can rule out the comma making an appositive phrase, and see that it must be a list comma, and we've got no ambiguity.
Putting in the Oxford comma makes it so we could interpret "My mother, Ayn Rand," as an appositive phrase, and we have ambiguity.
The presence of the Oxford comma, or lack thereof doesn't seem to affect the ambiguity.