Unfortunately, People will be disappointed with AMOL

Galad's father was never a King. And the rules of Succession in Cairhien seem quite complicated - Moiraine had two older sisters, yet she was considrered a strong candidate for the Sun Throne and the sisters had no support.

You are right. I had thought that Taringnail was Laman's brother, and has inherited the throne, but he was his nephew. I was mistaken.