As I remember it, the extra fee at York College was for any course in the nursing dept, including both clinicals and classroom classes. It would not apply to electives. That type of fee is common at many colleges, but is often hidden in the fine print.
I was able to plan ahead and give my daughter my old car when I was buying a new used car. There is a huge price difference between trade-in value and retail value, so it best to hand down a car to a kid when feasible. In that case, you also know that it was properly maintained. Fortunately, the hand-me down car didn’t die until one month after she was gainfully employed.
If you are concerned about fairness, you might treat the car as a loan, with the payment not required to paid until after she is working. You would probably keep the car in your own name anyway to save on auto insurance.