17 Year Old Wanting To Move Out In Arkansas

I have a 17 year old grandchild who lived with her Dad in Arkansas, whom recently ran away because of abuse in the home, the police picked her up and put her in juvenile detention for 2 weeks, brought her to court in chains, then put her on house arrest which put her right back in the same situation she tried to escape from. I live in Missouri and finally got temp guardianship, but the parents are constantly calling saying mean things to her and threatening to move her back home. The mother doesn't want her as she gave her to her Dad when she remarried. I've already enrolled her in school, took out health insurance, and bought her some school clothes. Is there anything we can do if her parents try to move her back and/or can her parents possibly pick her up and force her to go back to either one of their homes, or just take her? What is the age of consent in both Missouri and Arkansas for her to live on her own?

Who has legal custody?

I am not aware of any state where the age to move out without permission is under 18. I believe a loophole in the Missouri law (not in Arkansas) allows that it is unlikely any action will be taken if she (illegally) moves out at 17, but the legal age to do so is still 18.

the parents have joint custody, one lives in missouri one lives in arkansas.

Then parents have legal authority over her including where she lives. If Mom wont take her and Dad is abusive keep her with you long as parents agree