Governor Winthrop
Pearl is the daughter of Hester and Dimmesdale and therefore resembles their sin of adultry. Hester dresses pearl in a scarlet colored dress to show this and make her look more like the letter "A" which also resembles their sin.
Hester Prynne joins Dimmesdale in his vigil on the scaffold, holding hands with him as they watch the procession go by. Pearl also ends up joining them, refusing to leave Dimmesdale's side.
Dimmesdale interceded for Hester in the matter of Pearl's custody.
Some of the clues that Dimmesdale is Pearl's father include their physical resemblance, Pearl's strong connection and recognition of Dimmesdale, Dimmesdale's guilt and emotional reaction towards Pearl, and hints dropped by other characters such as Hester and Chillingworth. The reveal is confirmed towards the end of the novel by both Hester and Dimmesdale.
Hester explains Pearl's existence as a result of her love affair with Reverend Dimmesdale, emphasizing that Pearl is a symbol of their sin and their salvation. She believes that Pearl serves as a blessing in disguise, representing both the pain and the redemption that emerged from her relationship with Dimmesdale.
Roger Chillingworth approaches Dimmesdale just as he invites Pearl and Hester to join him near the scaffold.
Pearl continuously asks her mother, Hester, about Dimmesdale's connection to them. She questions Hester about why they stand separately from him, why he is reluctant to acknowledge them, and why he doesn't openly embrace their public shaming and punishment. Through these inquiries, Pearl is seeking the truth of their familial ties and the reasons behind Dimmesdale's actions.
Dimmesdale argues that Hester should be allowed to keep Pearl because she has shown remorse for her sin, the child could be a blessing in her life, and separating them would not benefit anyone. He believes that by allowing Hester to raise Pearl with love and care, both of them have the potential for redemption and a chance for a better future.
Before he dies, Dimmesdale stands on the scaffold with Hester and Pearl in front of the townspeople. When he does this, he reveals that it was he who committed the sin of adultery with Hester...
Hester -Pearl -Chillingworth -Reverend Dimmesdale
Dimmesdale acknowledged Hester and Pearl with surprise and compassion, but he could not openly acknowledge them as his family due to his position as a respected minister in the community. His emotions were conflicted between his inner feelings for them and his public image.
Hester and Pearl run into Rev. Dimmesdale on their way to the governor's house in chapter 7 of "The Scarlet Letter." Dimmesdale stops to converse with them briefly before they continue on their way.