His clinic may recommend a psychotropic rx to help with sleep and frustration. If he is not getting enough sleep, any cognitive difficulties will only be magnified. Sometimes rx can be presented as "helping you to do more of what you want to do." Other times it can be "Can you do this as a favor for me, so I can get more sleep and be better at doing [whatever he likes done] ?"
Driving -- could he become an official navigator, not just a passenger? Helping brainstorm mechanical issues, if he enjoys that? This could be anything from video games to hanging out at a repair shop to planning a classic car restoration. Of course, it can be presented as a neighbor, friend, relative asking him for help in a flattering way.
Technically, his doc can recommend that his license be revoked, but it sounds like that's not really the issue. As for searching the house for keys, your mom could tell him that they are off site and not to waste his time. She could then use a combination lockbox at a neighbor's, under the car...I think some cars can be modified to require a combination or password, also.
If he has had 3 accidents in 4 days, you certainly do not want him driving. What does he do when not looking for keys/questioning the diagnosis? It may take some combination of patience, drugs and creativity to rechannel what he thinks he wants to do.