What quotes show that the mother and daughter are alike in "Two Kinds"?
I believe this quote shows how Jing-mei and her mother are alike.
In fact, in the beginning I was just as excited as my mother, maybe even more so. I pictured this prodigy part of me as many different images, and I tried each one on for size.
This quote shows that both mother and daughter desire the fame and uniqueness of the child prodigy concept. Jing-mei likes the idea of being great at something in order to show off, and her mother likes the idea of having a daughter than she can show off to the world too. The similarity is pride. If Jing-mei winds up being a child prodigy, then both ladies will be proud of that fact.
Another quote that shows a similarity between the two family members is this next quote.
The girl staring back at me was angry, powerful. She and I were the same. I had new thoughts, willful thoughts - or rather, thoughts filled with lots of won'ts. I won't let her change me, I promised myself. I won't be what I'm not.
This quote shows Jing-mei's stubbornness. Jing-mei resolves to undermine every single one of her mother's attempts to make her a prodigy. For every doomed attempt, Jing-mei's mother resolves to find another way to make her daughter successful. Jing-mei's mother pushes harder and harder to make her daughter great, and Jing-mei pushes back equally hard. Both ladies are incredibly stubborn, and their attitudes eventually cause a complete break in the relationship.