Please help me with this friend situation?

I just ended a friendship because we kept fighting and and it really wasnt working. My parents were really proud of me because they didnt think i had the courage to do that, they lectured me about how it was for the best and how me and my cant talk to eachother anymore. they told me to remove her email from my contacts, and from my phone. My parents really hate my ex-friend. But my ex-friend just contacted me and told me how sorry she was and she didnt know how much she hurt me. I wanna be her friend again, but if i do, my parents wont take me seriously and theyll be disappointed in me. I dont know what to do. please help?