Buy and sell yu-gi-oh and/or pokemon cards, or whatever you kids are into these days, order them online (eBay, Amazon, craigslist) as cheapest as possible and sell them 10-25% higher. Of course keep track of what you spend, mail delivery costs, making the deals, etc.
Or collect plastic and glass bottles, and soda cans, smash the cans so you can save more and sell em once you have 20 lbs of it, slow but worth it.
Advertise to babysit, do chores for other people, clean homes, wash cars, etc.
"we don't live in a neighborhood" ? what ? since you live in nowheresville, you won't be able to get the cash like other 13 year old youngsters do
Mow/trim lawns. Big money it today. Mow/trim two lawns everyday at fifty bucks a day you do the math.....................