She cannot be forced to make an insurance claim but she is liable for the damage.
If she refuses to claim you need to establish either the repair costs and obtain those in writing from a garage or if the car is a write due to the cost of repair the value of the car again in writing.
Write a letter to her advising her that if she does not pay the amount within 14 days of the date of your letter you will commence County Court proceedings against her for the recovery of the sum plus costs and interest without further recourse to her. Make sure you add in any ancillary costs you have paid, eg. storage at garage if incurred.
You can then sue her online for the money debt.
Put money claims online in your computer search engine and it will come up look for the site that has .gov.uk for the official site as some solicitors try to get trade with similar named sites and follow the procedure.
As a small debt the claim will go through the small claims track which is relatively easy to follow. Once you have judgment you need to serve it on her and give a short period, say, 7 days for payment.
If she fails to pay there are various ways to enforce the judgment
Any further problems down the line come back to us for further guidance.
I hope this helps
If there are any further points please reply I will be happy to respond.