Why do you think Baker refuses to believe Stella has made progress with Frances? Do you think Baker deliberately uses the girl in her attempt to oust Mrs. Maynard? Why do you suppose Stella is willing to align herself with Baker again after such treatment?
Baker is extremely self-centered and will use anything and anyone to get what she wants. She is very manipulative and knows that she can influence Stella who is craving attention and affection.
Baker always has wily plans up her sleeve. She uses Stella because she is the most naive. She really doesn’t care whether Frances improves or not.
Francis has fooled everyone and no one has been able to get her to learn or demonstrate that she has learned anything. I think perhaps because Francis and Stella were about the same age, and Stella is kind and patient, she thought maybe something could work between the two of them. I think Stella trusted her again after she was accused of lying about writing the letters and the punishment because she saw it as her only way out. If you think about it, it worked to trust Baker again.