Childcare Expansion for Military Families Act of 2021 This bill addresses the provision of child care and development services by the Department of Defense (DOD) for children of members of the Armed Forces (military children). First, the bill requires DOD to establish a program to carry out minor military construction projects to construct child development centers, in amounts up to $15 million per project. DOD must establish procedures for the review and approval of requests from the military departments to implement construction projects for child development centers. DOD must conduct a comprehensive assessment of the availability of government-provided early childhood education and infant and early childhood mental health consultation services on and in the vicinity of certain military installations to identify and address the needs of military children. DOD is authorized to conduct one or more demonstration projects to evaluate improved approaches to the provision of educational and infant and early childhood mental health services to military children to evaluate the efficacy of such services to improve social-emotional development outcomes. DOD may authorize the development of a comprehensive professional development curricula for specified purposes. Finally, DOD must evaluate each demonstration project to assess the (1) extent of positive outcomes for military children, (2) improvements in services and continuity of care for such children, and (3) improved military family readiness and enhanced military retention.