If my niece was driving my car and bumped another car on private property so the cops couldn't give ticket, do we just fix our own damage?

Whether the owners of the two vehicles who were involved in a mishap on private land wish to repair the damages to each of their vehicles out of their own pocket, they can do so as opposed to making a claim with each other's insurance carrier assuming there is existing insurance.

Assuming the owners of the car wish to pay for their own vehicle's damages, I suggest that a written agreement be drawn up between the two owners to that effect dated and signed by each. Possibly a contacts attorney could be consulted for this project?