Here’s how we ultimately ended the battle; maybe it will help someone else whose parents are moving:
At about the time we were having the fight about Dad’s driving, we were also moving them from WA to CA, to live in an AL near me. A quick check of the California DMV website revealed that they’d have to get licensed within 10 days of moving, and that a road test would be involved (usually waived, but they didn’t need to know that). I gave them that information, and that ended the discussion once and for all. They sold the car before moving down here.