What motivates dimesdale and how reflects the relationship with her daughter?

Dimmesdale is Pearl's father; you asked about "her" daughter. Can you clarify your question please?

Dimmesdale's biggest motivation in the novel is guilt and shame. In Chapter 18, Hester finally shares the truth with Dimmesdale about her relationship to Chillingworth. From here, the two make plans. Dimmesdale's interactions with Pearl and Hester lead him to believe that possibly God has forgiven him. He admits that there was a time he'd been afraid of his daughter, that people would see his sin through her face (that she looked like him).

Pearl is confidant; Dimmesdale is terrified. Pearl holds all the cards; the love, the affection, the first move. Dimmesdale is almost childlike. In the end, he FINALLY sacrifices all for love of Hester and Pearl. He accepts his burden and relieves Hester; he gives an innocent, little girl back her innocence.

"For thee and Pearl, be it as God shall order," said the minister; "and God is merciful! Let me now do the will which He hath made plain before my sight. For, Hester, I am a dying man. So let me make haste to take my shame upon me."

Dimmesdale's act is ultimately more than he can bear, but through his confession he gains the love of a child, and the kiss he yearned for.