In The Scarlet Letter, was Hester a fit parent?
This is a tough question, and it has a personal opinion element in it as well. In developing your opinion, here are some things to consider. Hester refused to name Pearl's father leaving her to grow up in a single family home. Hester did teach Pearl her catechism even though Pearl did not answer questions correctly when asked by the Governor and Minister. Hester attempted to discipline Pearl, but Pearl's behavior was so crazy sometimes that Hester couldn't figure out what to do with her. Hester went to the Governor's house and fought vehemently for Pearl when it was rumored she might be taken from Hester. Hester was always honest with Pearl except the one time Pearl questioned why her mother wore the scarlet letter, and Hester lied saying it was because of the gold thread.
With respect to the Puritan culture of the time, no. Hester was a sinner, and did not raise Pearl with the Puritan's view of spare the rod, spoil the child. The town viewed Pearl as a demon-child, having witnessed tantrums, and strange responses the child makes. However, Hester does love her child, and is terrified at the prospect of losing her. While she seems at times obsessed with Pearl's actions, it can be seen that this comes from guilt, isolation, and inexperience.