Hands down, the best example I can think of is Avatar.
It helps that Azula always appeared cool and collected, it was her defining trait. Then, in the end, you begin to realize how off kilter her psyche really is. You see lack of self esteem, her guilt, and her desire to be loved by her mother. All these things existed before, but the audience didn't realize it until the end. After several betrayals, you begin to see the cracks in her persona, until everything comes crashing down around her, and she's writhing around on the floor like something filthy, disgusting, and pathetic.
It also turns the whole series into a family tragedy. Zuko wasn't the only character struggling to earn a parents approval. The psychological impact of his fathers actions tore everyone apart. It was a surprisingly mature theme for a childrens show, and it was a side plot that far exceeded the main plot.