If I'm 13 and I live with my mom but don't like the environment that I'm in, is there a way I could move in with my dad?

Given the circumstances that you have written about and your age, you are at a point to ask the court for permission to reside where you wish to reside assuming you have good reasons for such. Based upon what you have stated, either your parents sign a stipulation allowing you to move in with your father or your father files a petition with the court seeking an order allowing you to move in with him.