Nothing to do with your Car Insurance in my opinion. I just can't see the Insurers agreeing that it relates to the use of the car. The car was not in use as such. But you can give them a call to ask the question in general, but make sure the claim is not noted on the policy, if it is not something they would look at. Otherwise you risk having a claim event affecting the premium, even though they would never pay out.
The third party should claim off their own Car Insurance and it would be up to their Insurers to try to claim back of your Home Contents Insurance. The third party may also try to reclaim their excess this was as well. Home Contents Insurance includes personal liability cover, so if they agree that your wife was negligent they may accept the claim from the third party. Don't be surprised if your Home Insurers don't play ball, as there is normally an exclusion related to motor vehicles. The argument however, is that as the car was not in use at the time, it would not be a claim under Car Insurance, but a general issue of personal liability which may be covered under Home Contents.