Children's Ballet is a hidden skill that is acquired through the after school activities (Generations). You don't actually see sim children learning ballet, the activity takes place in the school rabbit hole for 2 hrs, 3 days/wk immediately after regular school so that's 3-5pm on Mon, Tues, Fri. As they gain the hidden skill, they should be able to show off some dance moves to the adults by way of social interactions. There should be a recital scheduled towards the end of the child stage. You might want to make sure your sim kids are actually attending the club at the scheduled times instead of just leaving school at or around 3pm.
You can check on the hidden skill to see if your kids are making any progress with MasterController (MC Cheats) as it will appear there along with all of the others.
Regular, on-screen Ballet is part of the Dancing skill for teens and older (although I believe children can learn it this way as well). It requires
this store set or the
Skylight Studio for the Performing Arts.