As the title says, I've got a nursery and I've got kids that I raised, the message on the side is now gone, where did the little tyke go?

If you paid 500 gold, then the kid is in another dimension maturing.

If you didn't modify  the standard value (through the "constants" mod), then the newborn will appear in your mansion in 10 days (if child), 15(if teen) or 20 (if adult).