The OP must pay for the damages, but I can't help but share a story from when I bartended at a golf course....
It was a really really REALLY hot day and there was only one group of avid golfers that decided to golf that day. They were literally the only ones out there. Next thing we know, a woman comes in--her windshield was hit, she was on her way to Fargo (4 hour drive) and it was Sunday. She couldn't see out of her window, and no place was open to fix it. The golfers eventually came in, but they adamently denied they had anything to do with it. Now, from my experience, these people were the stingiest (sp?) people in the world. They would skin a flea if they thought it would get them a penny. So of course, since we didn't have video proof, and the driver couldn't see exactly what the people that hit her looked like (understandable since a golf ball was flying at her), the course ended up paying the damages. Let's just say I was very upset with my boss for folding and taking responsibility.
But anywho, the OP is responsible. Pony up and just pay it. The sooner you're done dealing with the woman, the better.