What a blessing you are for her. Hopefully she will take the time she has with you to learn how to live a normal (not working the system) life. Best of luck and you really are awesome for doing this.
It sounds like you have a really good plan going. If going the adult ed route doesn't work for her, you should be able to get her enrolled in your local HS and into a credit recovery program.
While my situation wasn't as severe, my stepmother stepped in to help me out when my mom flaked out and left me homeless with barely any income when I was 21. I learned so much about basic living skills and setting goals in the 2yrs I lived with her. While my mom 'raised me' from birth to adolescence, my stepmother made me an adult who could succeed and keep reaching for more. You're doing such important work, and I hope you both find a positive relationship going through this experience!
You are doing a wonderful thing by taking her in. It sounds like she wants to get her life together by taking the CNA class and getting her GED. By having a support system like you and your DH, you are setting her up for success. I know it's going to be tough for a while but you'll all work through it and in the end you may have saved a young girls life from spiraling out of control.