The answer to your question lies in Chapter 32 and Chapter 33. In fact, a quote at the end of Chapter 32 illustrates Amy's capitulation to Lulu's demands:

“Lulu,” I said. “You win. It’s over. We’re giving up the violin.”

Amy's decision did not come easily. In light of the argument between Lulu and Amy in Chapter 31, we come to understand Lulu's sentiments; although she enjoyed playing the violin, Lulu didn't enjoy the pressure Amy put on her to perform at a certain level. If we fast forward to Chapter 33, we can see the reason for Lulu's stress and subsequent outburst at the restaurant. According to the chapter, Lulu had an orchestral concertmaster position as well as lessons with the Julliard-trained Miss Tanaka every Sunday in New York. Lulu was also required (by Amy) to spend long hours practicing every day despite her orchestral and academic responsibilities.

The conflict between Lulu and Amy stemmed from widely differing views about the role of accomplishment. To Amy, the violin symbolized control over one's destiny and 'respect for hierarchy, standards, and expertise.' On the other hand, Lulu viewed the violin as an instrument of oppression. In Chapter 30, we learn that Amy forced Lulu to play at her own Bat Mitzvah, and that was possibly the straw that broke the camel's back where Lulu was concerned. The instrument had ceased to bring Lulu joy; instead, it caused her an undue amount of stress and prevented her from indulging her love for tennis.

Here's another quote which explains Amy's decision in Chapter 33:

I couldn’t lose Lulu. Nothing was more important. So I did the most Western thing imaginable: I gave her the choice. I told her that she could quit the violin if she wanted and do what she liked instead, which at the time was to play tennis.

To reiterate, my best advice is to read Chapters 30, 31, 32, and 33 in order to get a fuller picture of Amy's decision.