I just realized that I haven't seen this mentioned anywhere else in the forum.
After your children max the 4 "child" skills, they can actually learn 7 more: Charisma, Fishing, Logic, Mischief, Piano, Video Gaming, and Violin, for a total of 11 skills.
They may be able to learn Fishing before maxing the 4 child skills. I haven't tried that yet.
When they become a teen, they drop the 4 child skills, but keep the other 7.