Does the Groomed to Rule lifestyle only get applied to children born after I take the perk?
I was eventually forced to unlock this perk to continue down the lifestyle tree, so I can confirm that this perk is immediately applied to all living children. Additionally, the perk has a chance to retrigger multiple times throughout your children's life (although I'm not sure what triggers is).
Based on the reading of the perk and my own experience, every time this perk triggers the child gets 1 random skill point, and the perk can trigger a total of 3 times (including the initial trigger).