I mean it really depends. Truthfully we don’t know if the real princess and the brother have a good relationship. We can imply that they do but we don’t know if it’s true unless you were to read the novel. Plus most people doesn’t acknowledge their siblings even if they are or aren’t blood related siblings. I think the problem is that she can’t just pretend to care about him since she knows they aren’t real siblings. Of course she could try but the raw feelings and emotions wouldn’t be there. It would just be fake. She could still try to form a relationship with the brother but i think she too busy thinking about herself and how to save herself from death.
also, to comment on something that the princess said in this latest chapter about the prince.
i dont really like the mindset she has for that issue. like even if you dont know him, you should still have a relationship with him bc he is the princesses brother. she cant just not acknowledge him bc he's not her real brother.