Yulia's impression of the king's relationship with his daughter is really judgmental. Of course he loves her as a precious memento of the woman he loved, but it's not like he doesn't love her or god forbid directing his desires at her. He's spoiling her and not expecting a whole lot from her as a result of that spoiling, but for Yulia to say he's keeping her like a "pet" keepsake of his departed concubine while she herself admits at the end of this chapter she's been clinging to the memory of the child's mother is hypocritical at best. She's "smart", so Yulia says, so she should be able to tell her dad she wants to do something.
Ideally, the king could be made aware that his daughter wants to do something positive for the good of the kingdom, or family, or whatever level she desires, but it just irks me that she just writes off the king's affection for his daughter that way. Maybe there's more to it that we haven't been graced with yet but I feel like the story was trying to make me agree with her position just from what has been provided thus far.
That said, I really love this take on the isekai villainess, since she can't directly control her actions, so avoiding that villainess fate is harder than simply "becoming a good person" every other one of these stories seems to leap on.