There are insurance policies that allow the insured to drive any vehicle - but that is the insurance policy she should produce, not her husband's which clearly does not insure her.
So, she need not be named on her husband's policy to drive his vehicle if her own insurance policy has the 'any vehicle' clause. She may be driving legally, but she has not proved this by giving you details of her insurance policy.
Report the accident to the police - tell them you believe this woman has no insurance.
Get on to your own insurance company - you pay them to handle claims on your behalf, if you are insured fully comp.