AITA for letting my daughter quit the family dance two days before the party?

My twelve-year-old daughter took off the ribbon we'd bought for her costume and said, "I'm not doing it if everyone keeps laughing."

Eight cousins were rehearsing a short dance for my sister's birthday party. My daughter volunteered three weeks ago. My sister chose the music, another parent arranged the steps, and I took the children to practice.

My daughter kept mixing up one turn. At the last rehearsal, an older cousin called it her "special solo." Some adults laughed. I laughed too, then saw her face and told them to stop.

At home she asked to quit. I initially said she'd made a commitment and the group needed her. She asked why her commitment mattered more than my promise that rehearsal would be fun.

I said she could step out. I told my sister immediately. She says the others now have to change the formation with only one rehearsal left, and that I should have asked them to stop joking rather than withdraw my daughter. I hadn't spoken to the parent teaching the steps before deciding.

My daughter is relieved. The cousin who made the joke has sent her an apology and asked her to come back. She still doesn't want to. AITA for letting her leave instead of giving the group a chance to fix it?