She familiarized her daughter with classical music.
Literal
She [topic-は] daughter [object-を] classical music [to-に] accustomed-made.
慣れ親しませた — 慣れ親しむ ('to become familiar with, to grow accustomed to') in its causative form means 'to familiarize someone with.' The compound combines 慣れる and 親しむ for deep familiarity.