How do I convince my mom to let me go to a ridiculously expensive boarding school across the border?

Just yesterday I found out I won a $10 000 scholarship towards an arts academy for getting 2nd place in a writing contest. The excitement lasted about five minutes. The thing is, I never even told my mom I was entering this contest, she has never heard about the school because I've never told her, and tuition costs $44 000. I'm pretty sure we could get more financial aid because we certainly need it, but how do I convince the woman to let me go? It's a high school, first off, but I'd only be going for the final year because I'm already in grade eleven. I live in Canada and the school is located in California. My sister is going to college next year that will set my parents back a good $40 000... so how can I get my mom to let me go? I'm sure I can raise, win, and earn over half the funds needed. My mom isn't the type of person to want me at home; in fact, we were THIS close to sending me to a school in ISRAEL last year. So what's up? What can I do? Does anyone have fundraising ideas?