Scenes will unlock as you progress in the game. If a scene is locked it is because you don’t yet have enough prestige to open it. Decorating and beautifying your island will give you prestige and once you have enough, the next scene will unlock automatically.

However, you must still play the scenes in order, and ‘Play Previous’ will appear beneath a scene that you have unlocked but cannot yet play. 
In order to play the final scene in the chapter you need to have gained 20 badges within that chapter. The only exception is chapter 1, where only 15 badges are needed.