Oddly, confronting her about her real identity, even if you use intimidation to get her to admit it, doesn't affect the character otherwise. Her relationship status with you remains unchanged, there are no further choices past her telling you the truth that relate to it, and she will still wish you a pleasant journey upon parting, even if you threatened to beat the truth out of her.
Solution: If you intimidate her, lower her relationship with you so that she is bitter towards you