There isn't a way to prove it now, and in Ontario we have a no fault system by default. Her insurance will pay her damage, yours will pay for yours. That's the way it is, even if fault was determined by an officer at the scene. She, ultimately, wants someone other than *her* to pay for her damages. So, she can go through her insurance and the insurance companies can duke it out (I do not recommend this unless damage is substantial), or take you to court. You can offer a settlement in writing, ensuring that your letter is without prejudice if you wish to negotiate, but really, the only fair solution is for each to pay for their own damages. That would be my only offer.
If she continues to be difficult, tell her that you will not pay for her damages and you suggest that the matter be taken to small claims court. If she begins to correspond in writing, respond with a dispute letter. In our dispute letters (when mediation has failed) we say something like this "this letter shall hereby serve as formal dispute your claim and suggest the matter be referred to the courts." We also double up our dispute letter with a sort of cease and desist, demanding that the receiver cease and desist from all contact save and except for written correspondence through Canada Post, and only then to advise of impending court action or vacating the claim. Court is the only way to determine who will pay, as she can't make you. If you can, avoid insurance. If the amount is relatively minor, keep it out of insurance hands. You will suffer for 6 years or more if insurance decides to increase your premiums. For a relatively small repair bill, it is not worth it.