What I see that both stories share is a self-awakening of each of the female protagonists in Amy Tan's "Two Kinds" and Ibsen's A Doll's House. I do not sense that they speak to a common theme of feminism.
While this is certainly the case with Nora in Ibsen's play, it is not the case with June in Tan's short story. By the end of Ibsen's play, which he insisted was not about women's rights but human rights, Nora has come to a new awareness—first about how she has been mislead into believing that her husband would sacrifice himself for her as she was willing to do for him; second, she becomes aware that in reality, she has never been valued for who she is in this male-dominated society: not by her father or by her husband. She has no rights even to try to save her husband's life. And when he discovers that she forged a signature to borrow money to save Torvald's life, he is not thankful for being saved, but furious that his reputation might be sullied.
I have existed merely to perform tricks for you, Torvald. But you would have it so. You and papa have committed a great sin against me. It is your fault that I have made nothing of my life.
Nora experiences an awareness of self that is galvanized by women's rights issues, but what is central to the development of her character is that she has never really known who she was—she lived first as her father wanted, then as her husband wanted, but has never been given to believe that she had the right to be her own person.
I believe that first and foremost I am an individual, just as you are.
In "Two Kinds," June struggles for self-awareness, but not in a male-dominated world: her struggle is to find her place while caught between the American society in which she is growing up, and the traditional world of her mother's Chinese heritage and her mother's slightly skewed perceptions of one's ability to achieve success in this new country.
Jing-Mei (American name, June) introduces this chapter of Amy Tan's collection of mother/daughter stories in The Joy Luck Club by identifying her mother's "American dream:"
My mother believed you could be anything you wanted to be in America.
However, soon after, June also notes how her mother believes she can achieve this dream for her daughter:
We didn't immediately pick the right kind of prodigy.
Watching talent shows on TV, Suyan Woo (June's mom) believes that her daughter can become successful by working hard to develop a talent. However, talent is something that is inherently natural to someone: a predisposition to succeed in a specific area. Though her mother tries, she cannot turn June into, for example, Shirley Temple.
June is excited about the being a prodigy at first, but failure dampens her enthusiasm. Her mother tells her there are two kinds of kids: those who obey and those who don't. Underneath it all, June believes she is a constant disappointment to her mom. Suyan tries to make June a child pianist prodigy, but June is not interested. Eventually they have a terrible fight, and June says awful things to her mother. The topic is dropped for good. As an adult, June feels she always let her mother down. It is not until after her mother dies that June realizes—in playing old piano pieces from her childhood—that while she did not measure up as she thought she should, she was still worthy: for her mother had never demanded perfection, but only a honest endeavor.
Who ask you to be genius...Only ask you be your best.