In The Scarlet Letter, was Hester a fit parent?

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.