I can't offer much advice on getting into the school... I auditioned for performing arts schools for Musical Theatre, but I didn't get in because I'm not a dancer. It seems like you've got that covered.

But I do have experience telling my parents that I'd rather study music and theatre than medicine like I'd always planned. My first bit of advice is to do some research. Learn what the different career possibilities are as a dancer. I know you want to perform, but dancing is very physically demanding, and you won't be able to do it forever, even if you stay healthy and don't get injured. Look into dance therapy programs, choreography, and things like that. Find out what it would take to do those (education, certification, start-up costs, etc.). Look into the statistics of dancing. What percentage of dancers who enter a professional training program (such as a performing arts school) actully go on to be professional dancers? How many of them are still dancing professionally after 5 years? 10? This is a lot of work, but I promise that if you show your parents that you are serious about this and know what you are talking about, they will take you more seriously.