Dear Lea,
You have my utmost sympathy. We went through all of this with Dad. Like Brenda's Dad, he did not have a diagnosis of dementia. He was always an erratic driver (came to live in the city on retirement - was used to quiet country toads before that) and got worse as he got older.
We tried everything - talking to him, talking to Mum, refusing to go in the car with him. It took months to get anywhere but eventually he was forced to give up driving - something he (and Mum!) could never understand or accept. It was a horrific time but I agree totally with Jennifer who says we must be concerned not only for the ones we love, but for other road users.
We tried some "emotional blackmail" on Dad, saying "how would you feel if you accidentally hit and injured someone?" but that didn't work either. It seems that the person is SO reluctant to lose their licence that they will stop at nthing to keep it.
In defence of my Dad (and almost certainly your's) they truly believe they are driving perfectly well.
When Dad had his RTA (like your DVLA) test, he thought he would get a perfect score
and was outraged to find he'd failed.
My suggestion is to write to your Dad's GP (keep a copy of the letter - you may need it later for DVLA) and set out ALL your concerns about his driving. Include the fact that your Mum is very defensive - this could be useful information for the GP.
Ask if he/she can set in motion some way of having your father properly assessed.
Best of luck with this terribly difficult situation.