Joint Custody in Divorce: A Quagmire

My parents, living separately for years, finally decided to get a divorce. However, they're both involved in my upbringing, and I live with my mom half the time and dad the other half. Now, they're arguing over who gets me on my birthdays and other special occasions. They both want to celebrate these days with me, but they can't agree on the schedule. My mom is insisting that I go with her every year, citing that she's been taking care of me on most of these days. My dad is opposing this, saying that he has a right to celebrate these special occasions with me. What legal remedy can the court apply in this situation?