Women in Apprenticeship and Nontraditional Occupations Amendment Act This bill expands the technical assistance provided by community-based organizations under the Women in Apprenticeship and Nontraditional Occupations Act to certain employers and labor organizations to include reimbursement for childcare and transportation expenses incurred by participants in apprenticeship programs. It also modifies selection criteria for grantees to require the Department of Labor to select not fewer than one employer or labor union from each state to receive technical assistance.