Certainly one should be free to discuss freely and frankly with parents, teachers, elders everyone. Nachiketa, Prahlad, Lakshman, Sita are all examples among many others. The criteria of choices should be truth (dharma) and not outer respect and forced obedience as we see in the case of Vibhisana, Rama, Krishna, Arjuna among many others. We always had a culture of free discussion based on how each one understood dharma, the cornerstone of Indian life.
I don’t think you could have handled better except that over the years one knows whether discussion is useful. If it is not going to be of any help in increasing mutual comprehension and understanding, especially if it is only going to worsen things then perhaps it is best avoided with a powerful silence as the main reply. Also pointing out her mistake was perhaps not a good idea. It only creates resistance and friction which only makes matters worse.
Affectionately,
Alok Da
