、。
Mother bought her a beautiful doll.
Literal
Mother [topic-は], she [to-に] beautiful doll [obj-を] bought-for.
やる (here in ~てやる) is the 'give outward / downward' benefactive — used for favors done for people of lower status or in-group children/pets. Contrast with あげる (neutral 'give outward') and くれる (inward to speaker). Using やる about a mother's action for her daughter is the normal, non-rude choice: parent → child is the archetypal やる relationship.