What is a quick summary of chapters 3 to 8?
Chapter 3 Hester in on the scaffold, and Chillingworth shows up in the crowd. He gives a false name, and indicates that she should keep quiet. He vows to find and destroy Hester's partner in adultery. Dimmesdale makes a plea to Hester to reveal the identity of her partner, but she refuses.
Chapter 4 Hester and Chillingworth have a meeting in the jail, where he takes part of the blame for her sin. He says he should not have married someone so much younger than he. He tries to convince her to tell him the name of the baby's father but she refuses. He insists that she continue to keep quiet about his true identity.
Chapter 5 Hester moves to an cottage on the outskirts of town. She wears the letter, and is an outcast. She spends time sewing fancy garments for the ladies of the town while wearing drab things herself. She also donates time to helping the less fortunate.
Chapter 6 This chapter focuses on Pearl, a willful child who is fascinated with her mother's scarlet letter. She has violent mood swings.
Chapter 7 Hester goes to the Governor's house because he has threatened to take Pearl. The house is described as very ornate.
Chapter 8 The Governor says Pearl will be damaged by her mother's sin, and Pearl refuses to answer his religious questions. Hester begs to keep her, and Chillingworth and Dimmesdale both agree. Pearl goes to Dimmesdale on her own, seeming to recognize him.
Put another way, once the letter has been placed on Hester, she goes about her life as best she can. Her ability to raise Pearl, though, is called into question by both her treatment by society and how she conducts herself as a mother. Between the two, the townspeople seem to have had enough of the little elf-child, and seek to have her removed from her mother. This section you stated ends with Hester fighting to keep Pearl, and ultimately winning.