Not to turn this into a parenting advice column, but shouldn't you be trying to get your kids outdoors on weekend afternoons? I mean, is it really productive for them to plop on the couch to watch a bunch of over-testosteroned guys driving their giant metal phalluses around an oval over and over again for three mind-numbing hours?
Turn left! Now go straight! Now turn left! Now go straight! I know of a great magazine that offers all kinds of fun information on your many outdoor options. It's called Outside.
Now, to answer your question: Don't expect to see NASCAR using biofuels anytime soon. Stock car racing didn't switch to unleaded gas until 2008, and its vehicles get somewhere between two and five miles per gallon during races. (Do the math: roughly 50 entrants for the Daytona 500, each burning about 125 gallons of gas equals 6,250 gallons of fossil fuels burned for the race. Oh the humanity!) The drivers don't use mufflers or catalytic converters on their vehicles, either. So enjoying a NASCAR race is pretty much the environmental equivalent of throwing a hunk of plastic on the campfire so you can watch the pretty rainbow of colors.
As for whether or not these vehicles could run on alternate fuels, I'd say yes. All race cars in the Indianapolis 500 have been powered by Ethanol for the past couple of years, for instance. NASCAR could make similar modifications, if it wanted to. Vegetable oil would have to be ruled out, because it only works with diesel enginesand strict stock car rules prohibit diesel engines. It's worth mentioning, though, that in 2008, Audi's R10 TDI became the first diesel-powered car ever to win at LeMans, so diesels can definitely be competitive in some races. Now click away from this page and search for a hike for you and your kids, or something. Maybe you can find one with all left turns.