The Family Stability and Opportunity Vouchers Act of 2026 creates a new housing assistance program designed to help families with young children escape homelessness and poverty. The bill authorizes up to 50,000 new housing vouchers per year from fiscal year 2027 through 2032 for eligible families, which include homeless or unstably housed families with children under age 6, or families expecting a child within 300 days, as well as families living in high-poverty areas or at risk of displacement. Public housing agencies that receive funding through this competitive program must offer mobility services to help eligible families move to neighborhoods with good schools or quality childcare, though families cannot be forced to participate in these services to receive a voucher. The agencies must partner with home visiting and support service providers where available and can receive additional funding to cover the costs of providing these mobility services. The Department of Housing and Urban Development must establish definitions and implementation rules within 180 days of the bill's enactment, with initial funding allocations to occur within two years of appropriation.