Phew!
If the registered keeper was not the driver, then they do not have to provide details of who was driving. In this scenario, the onus is on the parking company to provide the evidence.
If the registered keeper and the driver were one and the same person it would be madness for them to state that they were not driving and did not know who the driver was, as that is an out and out lie. It could be that the car park was covered by CCTV and if the parking company have a photo of the driver. If the reg keeper was taken to court and they were NOT the driver, they do NOT have to provide the details of the driver, even to the court.
However, if they are one and the same person and the parking company has a photo of them, the court (which would be the Small Claims court and NOT criminal court) would take a dim view of them having told lies, and would (rightly so) clobber them.
The point I'm trying to make to the poster of this question that if his wife was not driving, then she has no responsibility for this ticket, and no legal obligation to provide details of who was driving.
If the wife had been driving, I would have advised that she should pay up.