So I'm guessing the implication is that since Lady Remmington is looked down upon for being a woman, despite being incredibly competent, she intends to overwhelm her naysayers not only with her abilities, but also her children. She's probably thrilled that she has a competent daughter as an heir, but because she has grown to be rather bitter she doesn't tell her eldest daughter that.
Her youngest has it worse, since the younger duaghter Christine can't also be heir to the Remmington family, the mother probably intends for her to take the most powerful station that is available to her in the country. Crown Princess. That's probably why she had Lia kidnapped in the end. Lia and Christine are the only girls from the 4 families that are in the correct age range to marry Prince Nico.
As such, from her own vile perspective, she's not a traitor to the country. Getting rid of someone who undermines her own goals whilst also using them as a pawn in underhanded "negotiation" with another country. Two birds, one stone. That's why she doesn't see Lia as a person, but an object.
