Jaynes? Didn't you mean Aumann?
Sorry, my bad.
I think drilling for the reason might help. If you keep asking, innocently, playing a dumb devils advocate ("But what do you mean by X? How does Y justify Z? I don't understand why Q, etc.") and then you can at some point criticise her for believing in strange things that she can't explain to you in simple terms.
Roll up your sleeves and use the 37 ways words can be wrong, is my advice.
Orthogonal idea: Find some way to incite cognitive dissonance with her world view on the basis, perhaps, of object level morality.
On a personal note I happen to almost only interact with Traditional Rationalist or Very Sane For Common Man persons, so I have little practical knowledge of this.
From Being a Realist (even if you believe in God):
My mother, who doesn't call herself a theist (I think she's agnostic), doesn't even accept realism. She doesn't even agree with this:
That's little more than tautologies here. Yet it elicited an impression of being forced to believe. I know because she told me about the totalitarian dangers from such narrow thinking.
I'm happy to have finally found the root cause of our ongoing disagreement, but now, how can I deal with that? It looks pretty hopeless, but just in case, does someone have a suggestion, or should I just leave it at that? (My ego doesn't like it, but giving up is an option.)
Now I'm relieved to know that in near mode, she's a complete realist. This craziness only shows up in far mode.