Presumably she hasn't been deducting mileage ever for this business, and didn't depreciate the existing car.
Probably the simple thing to do is to start keeping a mileage, keep the old car, and start taking the standard mileage deduction - looks like $0.575 / mile or so. That will add up in a hurry, and she won't go through the expense of buying another car. So if she drives this thing for another 10 years, she can keep deducting that business mileage, long past when the car would have been fully depreciated. Given that she doesn't need to operate a truck or a luxury car to teach piano, this is the route I'd go.
The other option, as far as business use of vehicle is concerned, is to track actual costs. Keep records of all maintenance, gas purchases, etc. Then also keep a mileage log, because she likely won't be only using this for business. This option might work out at first, particularly if she buys the new car (depreciation), but once you've gone actual-costs on a particular vehicle, you can't go back to the standard mileage deduction.