In canon, the detection spells can't even tell the difference between Dobby's use of magic and Harry's. Telling the difference between a kid's magic and his parents' would appear to be even harder. For the wizarding kids, if their use of magic can't be told apart from their parents, there would be no way to sanction them. At that point the detection spells are only effective for muggle-borns. I'm not aware of any in-canon detection of children living with magical parents. (This would also let the wizarding families train their kids even when not at school, as a convenient way to bolster their status).