Just today you told me that the lady had suggested that it be enough for you to pay for the paint to cover the marks on her car. I think you should just tell the lady that you are going to file an insurance claim and ask for her insurance details if you haven't already. If she disagrees with your account of what happened, you can tell her that you will call the police and have them determine who was at fault. You have witnesses to back up your story so that part should be covered. Let the police state their opinion about who was at fault. If you have witnesses to corroborate your story and the police say the lady was at fault, you can go and file the claim. (You should, in fact, make the claim anyway just so that the damage may be inspected.) If she disagrees with the witnesses or the police, culpability will decided by the courts and it could turn out to be expensive for her. Now, I have no doubt in my mind that when the police hear the testimony of the witnesses and decide to believe them that the lady will admit she is wrong. She will only be liable to pay between a hundred or two as deductible and have lower insurance bonuses for a while. The brunt of the economic damage (between 1000 and 2000 euros judging by the sight of the damage in your car and hers) will be borne by your insurance companies. Nobody in their right mind will risk losing in court with such odds and with so little to gain.
Asked the police today and they told me it would be best for us both to pay for our own damages, that we are both at fault. We should have called the police to assess the situation on site.
So I called the other party and we decided to both make our claims and withdraw any blame on the other. I guess it is the best course of action, since the damages weren't that huge.