The answer is no, if she had an accident in one car, she would be obliged to tell the insurer of the other car as a material fact that would change her premium. On renewal, each insurer would want a confirmation of the no claims bonus from each other and would set the new premium accordingly. No telling the 2nd insurer at the time of the accident would probably invalidate the policy, and you would still have to tell them at renewal time anyway.
I can really see the benefit, you would be better to do as Ethel suggests and at least get the two car discount.
The alternative is to be a named driver on the 2nd policy, but you would still have some affect on the premium and would have to be honest about the proportion of driving in each vehicle or you risk the insurance being invalid.