We receive this question all the time on AVVO. Sit down and discuss your differences at length with your parents. You won't like the long-term affect if you move out on bad terms and you really don't have a strong legal position until 18.
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In order to change an existing custody order it is necessary to obtain a Judgment of Modification from the court. In Missouri, a minor can not simply decide to live with the other parent if the parent having custody objects. However, your custodial preference, is a factor in a judges' decision regarding a request to modify. The older the minor the more weight a judge usually gives to a minor's custodial preference. I am sure your mother loves you and wants what she believes is best for you and I am sure your father feels the same. Your parents need to discuss the issue and I hope jointly agree on what is best in your situation. A family counselor might help everyone with this issue. Take care.