How can one deal with a non-Muslim mother who practices sexual perversion, especially given her past kindness and her desire to visit her children?

The fact that the mother is a disbeliever or a transgressor does not prevent honoring her, which is an obligation. And among the greatest acts of honoring her is to continuously advise her to save her from disbelief and committing immoral acts. However, honoring her does not necessitate allowing her to enter your home with her partner, due to the great corruptions that would result from that concerning the upbringing of your children. There are multiple ways to honor her, such as inquiring about her, sending gifts, and visiting her alone to advise her and invite her and her partner [to Islam], without bringing the children, unless the partner is not present. It is permissible to boycott her if that affects her and prompts her to reconsider her actions; otherwise, continue to advise her and supplicate for her guidance.