Am i being a stupid teenager?

I want to move in with my dad who lives in southern California. I live in nor cal with my mom. The reasons for this include school, arts programs, opportunities, acting training, and my girlfriend. She lives there and I ean2 move and go to her school. My mom is utterly against the idea and says she would be an awful parent if she let me move for a girl. She says the chance we will end up together is tiny and that it's better that it's long distance because I can focus on school. I've been depressed for almost a year now since I only see her once a month. Am I being a stupid teenager? Or does my love for her make it ok?