There are dozens of Web sites that describe hundreds of jobs. Her reeducation should go toward retooling for readily available employment. Any level of computer work is in demand. If she's lucky enough to get a position, her overhead is free, the kids go to free local schools, and she works for board and other living expenses. Just because June should eschew public assistance doesn't mean she must go it alone.
Private organizations are out there to help.
Start with local churches and national and community-based charities. They help with child care, health care, reeducation. Aside from being more effective than most government programs, it's hard work to find and use them. That alone assures June that her dependency will be short-lived. I surmise that June already has plan that includes Washington.