If your daughter truly doesn't want to take the classes, I would let her quit. I wouldn't give her any hassle about it either. I wouldn't remind her of quiting ballet later. Here is my reason for this. When I was a child, my mother let me do anything I showed any interest in at all. I tried dance classes, piano, clarinet, Spanish for kids, drama, choir... My mother always told me that she never got to do anything, and I saw how hard she worked for me to be able to do those activities. My parents were divorced and she was working several part time jobs. By the time I was in high school I was still doing most of these activites, but I didn't excel in anything. It was frustrating for me to see my friends really truly enjoying being good at one thing. I enjoyed seeing my friends at each activity, but deep down inside I knew I would never be great at some of those activities. I just couldn't quit because my mom made me feel so guilty since she had never had the chance to do those types of activities. I'm very grateful for all the opportunities I had as a child, but I wish that I would have had a bit more freedom in choosing whether to quit. Kids are smart about what their potentials are. Your daughter is only 4 years old, and maybe one day she will be more interested in doing ballet than she is now. Don't push her, let her just have fun. Next time she is interested in something, see if you can do several trial classes first, rent the equipment for a short time, etc... As for the ballet classes, see if you can find out her real reasons for wanting to quit. Does she think she isn't good at ballet and it's just too hard? Is she being teased in class? Did she make a mistake and someone laughed? Did the teacher say something to upset her? Let her know that if she thinks she isn't good at it and practice won't help, that it's okay to quit. Let her know that if other kids are teasing her that you will try to stop that from happening. If she truly still likes ballet and is making mistakes resulting in the teacher being a little too strict or teasing from the other students, you can help her understand the importance of learning to laugh at our own mistakes and practicing. Just my two cents worth. I hope it helps.
P.S.- I did ballet as well. I think I was 6 when I started ballet. If you do make her stick to the ballet or if you find out she truly doesn't want to quit, don't let her start point too early. I was 10 when I started point, and I totally regret having started so early. Toe shoes really do a lot of damage to your feet. It's been about 18 years since I quit ballet, but my feet are still paying the price.