If you are an employee, your after-school is liable for damages you caused during employment. An injured child would likely to make an arugment that you are an employee just to get money out of school.
If you are an independent contractor, you are solely responsible for damages, not your school. If you drive students for multiple programs, it is more likely you will be treated as a contractor and school would not be liable in case of your accident.
How big is your so-called after-school ? Are they just mom and pop operation?