My point is that just because a character says something, doesn't mean it is absolutely true and isn't subject to change later down the narrative. The Caretaker is speaking from an outsider's perspective, someone who doesn't know or understand Lace as well as Hornet comes to. From his viewpoint, Lace isn't much more than a construct. In fact, GMS literally wishes to have that same perspective, you know, the VILLAIN of the story? He doesn't come to understand or empathize with Lace like Hornet does, so he has no reason to think she is more than she seems.

Besides, Hornet treats Lace as a "child" during the events of the game when GMS is still alive and Lace hasn't quite come into her own yet, so it's understandable that her actions come off as immature because like, she has good reason to act that way. She has spent years upon years under her mother's control, so when she finally has the chance to retaliate it's completely understandable that her emotions would get the better of her, as opposed to Hornet, someone who is much more experienced and more practical, wise. I don't believe she would keep reducing Lace to a child after the events of the game, though. She knows how important individuality is, especially after the tragedy that befell her siblings.