I am cracking up at some of these answers, but here's my attempt at a serious one:
$2,000 is £1,300 approx. You're unlikely to be able to make that in the time you're looking at (unless you have an established business), plus go to school, plus do home work, plus have a life.
You could move in with someone either renting (might be a bit young to get landlords looking you seriously) or a mate. Or other family?
And for money get a part time job or work on your biz until you make money. As other people have said offer writing services to start with...etc.
Or you could just suck it up and move with your family. No offence, but you are 17 and aren't even considered an adult yet according to the law. Might be a bit early for you to be striking out on your own. When you're 18 you can do what you like.
If you move now, since the school year has just started you can probably pick up where you left off in a new school although it's never usually great starting somewhere new, especially a completely different area.
Unless you've already answered this, I have to ask why are they moving out of the area and think it's a good idea for you to change schools? A Levels aren't exactly easy at the best of times, especially if you have to settle in to a new area.
What are you studying by the way, and what do they want you to study? It's not really their decision what you study, but depends what you've chosen, maybe they have a point. How were your GCSE results?
If you do A Levels at college/school during the day and work a shop job in the evenings, you can maybe earn enough each month to pay for a room, for food...etc. Might be a bit tight, but you'll probably be the only person in your school with their own place...
Or you could take a year out, work full time to pay your own way and build up savings, and go back to school or college a year later to finish off your A Levels. Being put back a year isn't the end of the world when it comes to A Levels, I know someone who did that (failed A Levels first time round) and he's done fantastically - got a degree, good job earning £60k+...etc.
Why do you have the figure of $2,000 in mind? If you rent a single room and eat baked beans, you can maybe squeeze by on £700 or £800 a month. Depends where you are in the country though.
Don't know if that helps at all. Probably not.