I'm very familiar with your situation OldViking, except it was with my late husband (died 3 years ago at 78).
He developed congestive heart failure after being very ill with multi-organ failure 3 years before his death. He had been due to have a bypass, but that was cancelled because the risk outweighed the benefits, so was on various meds to control his condition. He was on BP meds as he also had pulmonary hypertension, and began to have occasional fainting events (vasovagal syncope maybe), especially after getting up from a chair (orthostatic hypotension). These gradually became quite frequent, over the following 3 years, until it was almost daily.
Then one day he blacked out while driving a brand new car, and hit another car (fortunately no injuries to the other party) but he had became a terrible driver in the preceding years. He was admitted to hospital, and after tests, was found to have a small bleed on the brain (no doubt caused by the falls). This also resulted in short term memory loss, a bit like dementia.
He came home, but it was extremely difficult to cope with him, as like your Dad, he was a stubborn old bugger. A week or so later, he had a bad fall down the stairs whilst I was out shopping, and I came home to a blood-soaked hall. Straight back into hospital, where he slowly deteriorated, and died 2 months later (from pulmonary embolism).
Like your Dad, he was a life-long smoker, used to do weight training (very vain!), and liked to drink, even when he was quite ill (he became quite jaundiced near the end, from liver failure). So I know where you're coming from, unfortunately.
He really needs to stop driving, hard as that is, as he's at great risk of an accident - does your Mum drive? I took over most of our driving long before he became so bad as his driving frightened me, but he still went out and about alone in the car.
He absolutely must go back to his doctor, could your Mum go with him? It must be very hard for her to deal with this, and I'm sure you will try to support her as much as you can.
Wishing you the best, good luck!