This paper studies the interaction between parental and public inputs in children's skill formation. We perform a longer-run follow-up study of a randomized controlled trial that increased preschool quality and initially improved skills significantly for children of all backgrounds. There is, however, complete fade-out for children with highly educated parents. Given positive long-run effects for children with low-educated parents, the treatment reduces child skill gaps across parents' education by 46%. We show that the heterogeneous treatment effects are a result of differences in parents' responses in terms of investments, reacting to school quality later in childhood. There is also evidence of cross-productivity between reading and math skills and socio-emotional development.