If she's arguing from a position of separate magisteria which have to be reasoned about differently, I would probably try this tactic. Point out that we do not automatically gravitate to reasoning correctly about mundane things; you can use examples from Greek philosophers and alchemists and so on. Correct processes of mundane reasoning are something we've had to develop over time by refining our methods in situations where would could tell if our conclusions were wrong.
That being the case, how does she know that her different procedure for reasoning about non-mundane things is one that works? If it were simply wrong, how would she be able to tell? If her procedure for reasoning about non-mundane things can be used to draw contradictory conclusions (it almost certainly can,) point out that you have on the one hand a set of confusing apparent contradictions that must somehow all be true, and on the other hand the possibility that the reasoning procedure simply doesn't work.
If her procedure for reasoning about non-mundane things can be used to draw contradictory conclusions
From what I read, the procedure for reasoning about non-mundane things is used to avoid drawing any conclusions whatsoever, much less contradictory ones. It's intellectual cowardice masquerading as deep wisdom. (Sorry for dissing your mom, loup-vaillant.)
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.