We study the design of child-care policies when redistribution matters. Traditional mothers provide some informal child care, whereas career mothers purchase full time formal care. The sorting of women across career paths is endogenous and shaped by a social norm about gender roles in the family. Via this social norm traditional mothers' informal child care imposes an externality on career mothers, so that the market outcome is inefficient. Informal care is too large and the group of career mothers is too small so that inefficiency and gender inequality go hand in hand. In a first-best world redistribution across couples and efficiency are separable. Redistribution is performed via lump-sum transfers and taxes which are designed to equalize utilities across all couples. The efficient allocation of child care is obtained by subsidizing formal care at a Pigouvian rate. However, in a second-best setting, a trade-off between efficiency and redistribution emerges. The optimal uniform subsidy is lower than the "Pigouvian" level. Conversely, under a non-linear policy the first-best "Pigouvian" rule for the (marginal) subsidy on informal care is reestablished. While the share of high career mothers continues to be distorted downward for incentive reasons, this policy is effective in reconciling the objectives of reducing the child care related inefficiency and achieving a more equal income distribution across couples. Our results continue to hold when the social norm is defined within the mothers' social group, rather than being based on the entire population.