"要和他们主管商量下给我电话"

Don't give up so quickly. If I were you I would try to talk to this teacher again and ask her/him give your daughter a chance just for trying a week. At same time have other preschool spot ready for your kid.
I would talk to the 主管 too if I got a "no" answer from the teacher but talk to the teacher first.Show funny story, cute saying...about your daughter to the teacher. For me I feel telling my kid story is so powerful to change teacher's mind. Good luck.