Vancity, this is Myrna. I can tell you first that I am a licensed clinical social worker and a licensed professional counselor, and I am older than both your parents. So, you are getting feed back here from a professional with over 30 years of experience, and you can take this to your parents and tell them what I am about to say, if you wish.
This is about your right as a young woman to maintain your personal integrity. I could see your parents being upset if your skirts were too short, or your clothing was too revealing. However: you were born with curly hair. What you need to tell them is that they are pressuring you inappropriately. So: if you cave to inappropriate pressure, what is going to happen down the road? will their expectations set you up to cave to sex, drugs and rock and roll? I am serious here. We women, of all ages, need to know when to put our feet down and say NO. "NO, mom and dad, this is my hair, the hair that G-d gave me, and if you dont like it well I guess that is OK. But I am not going to compromise my personal integrity just because you dont like it. "