AFAIK there's no rule saying you need to repeat the preposition before each item in a list; if there were, the sentence with the serial comma but no appositive would need to be "To my mother, to Ayn Rand, and to God."
The parallelism exists in order to deal with the aside, not because it's necessary for every element in the list. But putting aside that debate, here's the thing. You can't fix "to my mother, Ayn Rand, and God" by removing the comma. It's still ambiguous, indeed nonsensical. You fix it by adding "to". That is, the serial comma is not what's creating ambiguity, it's the omission of a word.
But the ambiguity in "To my parents, Ayn Rand and God" is fixed by adding a comma. That is, it's the missing comma that's the problem.
Typically, you would only repeat the preposition for emphasis/effect or if it varies for at least one element—e.g., for the latter, "I wrote to my mother, to Ayn Rand, and for God."
