Captain Keller strongly disapproves of Annie's work with Helen. In short, he feels that Annie is too strict with her charge. He believes that Annie lacks pity or compassion for Helen. To Captain Keller, Annie is unsuited for the position she has been hired for.
In act 2, everyone is having dinner when Helen reaches into everyone's plates. Captain Keller tells Annie that Helen must be allowed to do as she wishes at the table. In other words, he believes that everyone should humor Helen, however annoying her dinnertime habits.
When Helen reaches into Annie's food on her plate, the tutor thrusts her student's hands away from the table. This occurs a few times until Helen launches into a full temper tantrum. During the power struggle between Annie and Helen, the latter bangs her toe. The text tells us that Helen cries with "rage and feigned injury."
Meanwhile, Annie holds on to Helen's wrists. For his part, Captain Keller orders Annie to let go. However, Annie argues that Helen must be trained out of her ugly behavior. Captain Keller is so angry at Annie's insubordination that he tries to dismiss her from his employ. However, he eventually decides to give Annie another chance. Without Annie, Captain Keller knows that he would have little choice but to send Helen to an asylum.
During their conversation, Annie demands complete control of Helen until the young girl learns to submit to her authority. Captain Keller balks at her terms but eventually decides to give her two weeks.
All in all, Captain Keller deeply dislikes Annie's methods. However, despite his doubts, he decides to give the tutor another chance. Captain Keller has a greater fear of sending Helen to an asylum than of Annie using what he considers objectionable methods to train her charge.