What's the internal and external conflict between Waverly and her mother in "Rules of the Game"?

This story is really one big struggle for independence
between Waverly and her mother. Waverly, as the story progresses and she becomes more
aware of her talent, shows embarrassment at the way her mother takes pride in her and
wants to exploit her gift and talent to bring attention to
her:

My
mother would proudly walk with me, visiting many shops, buying very little. "This is my
daughter Wave-ly Jong," she said to whoever looked her
way.

One day, after we left a shop I said under my breath,
"I wish you wouldn't do that, telling everybody I'm your
daughter."

While the narrator
enjoys the challenge of winning at chess for its own sake, clearly the mother enjoys the
success of her daughter for the admiration it brings to
her.

At the end, the imagery of the chess board in
Waverly's dream is used to symbolise the conflict between Waverly and her mother, as
each struggles for mastery over the other. The way that the story ends, with Waverly
closing her eyes and "pondering my next move," indicates Waverly's desire to escape her
mother and treats her conflict as a game of chess. Although Waverly has lost this round,
she is considering how to eventually beat her mother and gain the independence she so
desperately desires.