Children do have privacy rights, just like adults, although because of their minority status, the rights of children are limited. Whether three years old, or 13 or 17, knowing where your child is and what they are doing is a parents number one priority and your parental legal right.
Children are expected to obey their parents and the legal system supports the parent's rights to enforce this (except in instances of parental neglect and abuse). The issue of invading a child's privacy tends to arise in other areas, like with health records or collecting data, and not in parental rights to protect their children.
