How can a runaway put a restraining order on her mother?

That's not possible. But it is possible and legal for the parent of an absentee minor to hire private agents to track down the minor and return him or her to parental custody, Likewise a parent can request that the court issue and order to have the minor returned to their custody or to custody of their home state. Once a court order is in place authorities will be on the look out for the minor and will take them into custody and remand them to state juvenile authorities.