Is it permissible to interact with a woman as a Mahram after discovering that she is not, yet she has a strong connection to the family, and she has been treated as a Mahram for a long time based on a mistaken belief?

If this woman is not your suckling maternal aunt (khalah from rada'ah), then she is a stranger (ajnabiyah) to you, and she must be treated on that basis. It is not permissible to kiss her hand or shake it, nor is it permissible for her to uncover herself in your presence. If she becomes an old woman who is no longer desired, then she has other rulings. If your mother told you that she is your aunt (khalah) and that was not the case, then she must repent. It is important to be aware of the seriousness of being lenient in these matters related to Sharia rulings.