Why was Sarah so upset at the No Tones performing?

I thought the poker game made her furious later on. She mentions in her speech later, "she will play with poker, be with me, learn to speak--that's all you, not me."

My guess for the No Tones performance is that she thought James was humiliating them. That they looked foolish and everyone was actually laughing at them, rather than cheering them on. Notice how, on their date, she tells James how she thinks Lydia looks terrible while learning to speak.

Sarah was upset when she saw the No Tones because everybody was amazed by them and she felt excluded. James had been pushing for her to speak but she refused, and even mocked the way Lydia talked (the restaurant scene) - but then she saw these kids actually dancing and singing, and the audience were loving it, it must have touched a nerve. The kids were adapting, as you said, but she wasn't. Sarah didn't want to adapt, she just wanted to dwell in her bitterness, which is why she initially gave James such a hard time when he tried to get to know her. The fact that James was so visibly proud of the No Tones just made it worse, most likely because she thought he would never feel that way about her.