Pearl is an unusual child born in unusual circumstances, and that is true from the first time we meet her in her mother's arms as Hester walks out of the prison door on her way to the scaffold all the way to Pearl's happy, "normal" life of riches and nobility in the Old World. In The Scarlet Letter by Nathaniel Hawthorne, Pearl speaks about things she does not really understand, and that includes the times she speaks to her parents, Hester Prynne and Arthur Dimmesdale.
Pearl is a precocious, even for a Puritan child, probably because her only companion and teacher is an adult, her mother. She seems to innately understand that her mother is wearing a letter which represents some sin she has committed.
“Mother,” said little Pearl, “the sunshine does not love you. It runs away and hides itself, because it is afraid of something on your bosom...."
Not only does she recognize sin in her mother's life, but she also recognizes it in Dimmesdale's life--and she recognizes that their sins are the same. She understands that Hester wears her A "for the same reason that the minister keeps his hand over his heart!" This indicates again her ability to sense sin in others, particularly her parents.
Pearl intuitively connects her mother and Dimmesdale, and several times in the story when the three of them are alone together (which of course is not often), Pearl asks Dimmesdale to stand with her and Hester out in the open, where everyone can see them. This is a call to public repentance, especially for Dimmesdale.
In chapter twelve, when she and her mother discover Dimmesdale on the scaffold, Pearl is happy to join him up there as Dimmesdale asks her to do; however, she asks something of him, as well.
"Wilt thou stand here with mother and me, tomorrow noontide?" inquired Pearl.
Of course Dimmesdale politely defers, but Pearl is adamant:
"But wilt thou promise," asked Pearl, "to take my hand, and mother's hand, to-morrow noontide?"
When he still refuses, Pearl scolds her father:
"Thou wast not bold!--thou wast not true!" answered the child. "Thou wouldst not promise to take my hand, and mother's hand, to-morrow noontide!"
Clearly the little girl recognizes the minister's need for repentance, though she certainly would not have used that word. What she does know is that for the good of them all, he should admit to being part of this sad little family; when he will not do it, she is disgusted with him. She tries again when the three of them are in the forest, but the result is the same.
What Pearl does not realize is that if Dimmesdale were to agree to her request, Pearl would probably have had to then convince her mother to join them--not because Hester is ashamed of loving Dimmesdale but because Hester has not repented, either. Though she has been punished, she still wants to be with a man who is not her husband. If their relationship were made public, that would not be possible for her. We know that the one time Dimmesdale does claim Hester and Pearl, Hester is the one who does not want to make this public claim, as it means the end of her dreams for them to go away and be together.
Pearl makes the pointed statements and asks the uncomfortable questions of her parents, comments and questions which should provoke them to repentance; however, there is no repentance made except by Dimmesdale at the very end of his life. That is a breakthrough moment for both father and daughter, ensuring that both of them can live and die in peace.