The excerpt below is from the book "Media Law for Journalists", chapter 2.9 "A child's right to privacy" re: an appeal case.
It is about children being photographed by paparazzi, but touches on a couple of things such as a child having a greater expectation of privacy than an adult in day to day life, a child's right to privacy being distinct (though not entirely separate) from that of the parents, and parental conduct and motive being a consideration in whether an interference of privacy is justified. Just posting this as general food for thought.
What I feel we are missing (in society in general, not on here) is that many of the biggest threats to a child's privacy in the social media age come from people WITH parental responsibility.