How is the scaffold symbolism in The Scarlet Letter?

There are three main scaffold scenes in the Scarlet Letter. The fist is in the beginning of the novel, when Hester has to go up on the scaffold with Pearl in front of the entire town. The second is in the middle of the night, when Hester and Pearl find Dimmsdale on the scaffold. Pearl stands between Hester and Dimmsdale, holding both their hands and linking them together. The third scaffold scene is at the end of the novel when Dimmsdale asks Hester and Pearl to join him on the scaffold in pulblic, during one of his sermons. He confesses his crime and Pearl finally finds out who her father is.

These scenes are used as a unifying device throughout the novel. In the first scene, Hester and Pearl are unified together, in front of the rest of the town. In the second scene, Pearl is the link between Hester and Dimmsdale, which brings them together - except it's in the middle of the night, so it isn't public unification. In the third scene, all three are united together on the scaffold, in front of the whole town. In that scene, Pearl's life id fulfilled because she knows who her father is, and Dimmsdale can finally stop suffering internally because he confessed.