You can simply just stay silent/let her do whatever and skip any checks and she'll spare Dame Aylin. I've heard this can differ based on your approval, but it makes sense to me given what we later learn re: her past
Really? They do take your approval into account? But not if you fail a persuasion check? I hope I still have a save to try as I had her at 100%. If it is so, I wish they fix it and default to the same approval check.
EDIT:
Damn it, just tried it from an old save. My propensity to save scam took the better of me, LOL.