Having worked alongside our NHS Teenage Pregnancy team for a while, in a part of the country with a hihg incidence of schoolgirl mothers, this seems to me to be a sensible mother protecting her child, if the child is going to do it anyway - but what a message it's giving out to other kids. Both children are under age for consent, but I daresay that these days they are only doing what other youngsters are also doing. We can't compare it with when we were their age (I barely knew what it was all about at the age of 12!) and public views and mores have changed so much. I still remember going to my GP for contraceptive advice when I was 19 and engaged, and my GP told me that I ought to wait until I was married, and "what would my mother think?"
I don't like the story in this post, but at least it is better to be safe than sorry if the young girl couldn't be persuaded to bide her time. A parent I know prefers that relationships with her (admittedly a little older) children happen at home, too, rather than scruffily round the back of the bike shed.
As rowan says, one only hopes that they are both aware of the dangers of STIs which are prevalent in younger people these days.