Child Welfare; Requiring the Department of Children and Families and Department of Juvenile Justice to identify and meet the needs of dually-involved children within a specified timeframe; revising information that must be included in a transition plan; requiring prenatal and infant health care delivery programs to include certain father engagement activities; requiring the Department of Children and Families to contract for the development and implementation of the Responsible Fatherhood Initiative and to provide grants to community-based not-for-profit organizations to offer certain mentorship programs; designating the month of June as "Responsible Fatherhood Month", etc.