Why Azula playing these games? Why did she ask Zuko to join her side, instead of just being upfront about it, and take Zuko and Iroh to prison?
Very simple, drive a wedge between Zuko and Iroh. The only friend Zuko had was Iroh. And Azula wants to take that away also, so Zuko has nothing.
If I am right, Azula is one sick twisted person.