Why it is "své matky" and not "svou matku"?
Vážit si uses the genitive. Svou matku is accusative.
Is it possible to use: Žofie appreciates her mother?
I think it should be
I think so too. Vážit si seems to mean to hold someone in high regard. That may usually imply respect, but those two are not interchangeable. Já mohl bych někoho respektovat ale nevážit ho. No?