OP, this is a legitimate and essential procedural issue and is wholly relevant.
Motobility are not the registered keepers of their vehicles, the keepers are the persons with whom they have their contract for the supply of the vehicle. If your wife is able to conduct her affairs, then this would be her.
In which case the NTO would have been addressed to her and only she can appeal to the adjudicator. She may authorise someone else in writing - fairly commonplace- but this authority must exist.
We just don't want to see her getting to adjudication, in the guise of you, only to be told you cannot represent her for want of proper authority.
The registered keeper is the person whose name is registered with the Driver & Vehicle Licensing Agency in Section 5 of the vehicle's log book or V5C. In the case of Motability Scheme cars, this is the customer.