I had this issue with my dad years ago.. He had the onset of dementia, and his driving became very erratic..
My SIL said that their children were no longer allowed in the car if he was driving..
My mum was too scared to tell him (didn't want to upset his feelings, not scared of him). so when he was complaing one day about something to do with them, I told him what SIL had said, and that I agreed...
He was furious, spouting that he had never had an accident in 40 years of driving (and he hadn't) but my mum and I managed to persuade him in the end..
It is hard, especially as my dad knew he had dementia and what was likely to happen to him, it was a stand against losing his indepdence I think..
Personally I wouldn't nag your mum to much, if your dad has got dementia she will have enough to cope with...
I would say don't worry about hurting his feelings and let him know that you just don't think he is safe, and you wouldn't let him drive your children around.. And also say that it is his illness causing his irratic driving, not him being a bad driver. (I am sure that is what made my dad stop)...
good luck