The summons reason is ‘For a case management hearing (deft to attend). What does that mean?
A case management hearing is one held in advance of the trial. Its purpose is to identify what is agreed and the issues in dispute. In more complex matters it is also used to determine which evidence can be simply read to the court and which witnesses need to attend to give evidence in person, to be cross-examined if necessary. Finally an estimate of the time required for the trial is made and a date is set.
The issue is straightforward - did your wife exercise reasonable diligence in an attempt to identify the driver after receiving the request? The prosecution evidence should not be in dispute. It will consist of evidence that an offence was suspected, that a s172 request was served and a reply, failing to name the driver, was received. I'm surprised a case management hearing is deemed necessary, but that's a matter for each individual court.
Water under the bridge, but since you have seen the photographs that the police have, which did not help identify the driver, it is unlikely they had anything else which did. So your worries that they might would have been unfounded. Even so, in the event that the wrong driver was nominated and the police can see that (this would usually be a male nominated and a female seen in the driver's seat, or vice versa) they would have been unlikely to have prosecuted your wife for making a false statement. Instead, provided they did not suspect her of attempting to pervert the course of justice (say if one of you had nine points and the other none) they would usually simply ask if she wished to "reconsider" in the light of the photographs.
It is usually possible to do a "deal" with the prosecutor to plead guilty to speeding if the "Fail to provide driver's details" (s172) charge is dropped. As above, this can only be done when the person charged is the driver and usually (though not necessarily) when they have been charged with both offences. This deal is often undertaken when the recipient did not receive the request or did not respond to it. You haven't said whether your wife has been charged with both offences but I have a suspicion she might not have been, in view of her response to the request. Quite how a prosecutor would react if your wife suggested such an arrangement, when she has stated categorically that she was unable to say who was driving is difficult to say. It might be worth delicately broaching the subject.