I tried a new dentist and was not happy with the experience. New dentist said the crown needs to be redone.

She put in crowns and I later switched to another dentist. I have much sensitivity to cold/chewing. My new dentist said the crown needs to be redone due to a gap/poor crown work. My new dentist contacted the old dentist to request a refund. The old dentist said she would redo the crown, but would not honor any refund if another dentist performed the work. Is this normal? She did a poor job the first time, I don't want to go back to her. What are my options? Thank you.