[tzs]

Good example.

Without the Oxford comma, it is unambiguous because we know that the comma cannot be making an appositive phrase, because if it was that phrase would include "Ayn Rand and my daughter". We know that your mother cannot be your daughter, so that cannot be intended part of an appositive phrase.

Note, though, that it is only unambiguous without the Oxford comma because we know that one's mother cannot be one's daughter. So in some sense it actually is ambiguous grammatically but we can resolve the ambiguity by using knowledge beyond grammar. (I don't know if punctuation counts as grammar, but I'm counting it in this comment).

As with my examples, the ambiguity stems from comma being both a list separator and a separator for parts of appositive phrases.

If we were to write appositive phrases like I suggested (using parenthesis instead of commas), and always use the Oxford comma, it would become "To my mother, Ayn Rand, and my daughter" and would be grammatically unambiguous. We would not need to know the meaning of the words to parse it. We would only need to know their grammatical categories.

[cryptonector]

I think you're quite right that mixing different separator uses of the same punctuation character is a source of ambiguity. This is where em-dashes and parentheticals shine.

It's also a good idea to rephrase to avoid the ambiguity. E.g.,

    To my mother, Ayn Rand; and also to my daughter, and God.

or

    To my mother, to Ayn Rand, to my daughter, and to God.

It's not always possible to just sprinkle a comma to disambiguate, so don't just do that. Use other punctuation. Add punctuation diversity to your writing -- make it clearer and more fun for you to write, and others to read.

The trick is to notice these issues as you write. Of course, that's not always easy, and it's particularly difficult when speaking, but at least it's not usually expected when speaking.

[vidarh]

When speaking, we will also often address it by changing intonation and shortening pauses to indicate that we're interjecting something rather than continuing a list. E.g. in this case adding pressure to "Ayn Rand" and shortening or cutting the pause implied by the first comma if we want to imply they're one and the same:

To my mother Ayn Rand, my daughter, and God.

And if we sense ambiguity we'll often similarly extend subsequent pauses to clearly separate list items.

We'll also often add body language to make the emphasis on connections even stronger.

I'm guessing a lot of ambiguous written lists are ambiguous because people have written the words roughly how they'd said them, and tried to follow grammar rules without thinking about the extra cues they're leaving out that'd be there if speaking.