Your son's mother can indeed change her mind if she chooses to do so. Whether a court will send the child back to her is another question. Being that the child is 13, he will most likely be assigned a lawyer who will represent his interests in court. If he wishes to stay with you, his lawyer will represent this to the court and the court will consider his choice considerably. The legal standard is what is in the best interests of the child. Many factors can determine how a court will rule, such as how the child came to live with you, the fitness of each parent, drug or criminal history etc. You can file a petition for custody in the family court, or you can keep the child, and if the mother wants him back, she can also file a case. Hope that helps.