This would depend on state law. Some states cover an automobile under Castle Doctrine and do not require a permit for carry in the vehicle.
If yours is a state that does require the permit, and your wife is operating the vehicle, and you are not with her I believe she could be charged or ticketed for carrying without a permit.
Again, depending on the state this can be quite serious as some states have felony penalties for convictions of carrying without a permit. This would not only prevent her from having a gun, but you as well, since you two are in the same house. You should look for the laws of your state concerning carrying weapons and thoroughly review them. Cops also are not a good source of law info as they often get it wrong (from experience).