This question has no single correct answer.  It's going to be different for different readers.  I have read "Two Kinds" many times.  My reaction to Jing-Mei and Suyuan's conflict changes.  

The first time that I read the story, I completely supported Jing-Mei, her attitude, and her actions.  Of course I was an opinionated, high strung, teenager the first time that I read it.  I thought that I knew everything.  I thought that my parents didn't know anything, and I thought that they were out to ruin my fun by making be something that I didn't want to be.  Jing-Mei's character resonated deeply with me, so I sided with her.  

Of course now that I've been teaching for thirteen years and have three children of my own, I don't side with Jing-Mei anymore.  Suyuan's character is much more relatable to me now. She wants her daughter to work hard.  She wants her daughter to use all of her natural talents.  She wants to help Jing-Mei be the best that she can be.  I get that.  That's what I try to coax out of the athletes that I coach, and I have some that just don't want anything to do with it.  It's frustrating, which is exactly how Suyuan feels.  That's why now, I react with much more understanding and sympathy toward Suyuan, and I get frustrated and a bit angry with Jing-Mei's stubbornness.