Are both antihypotensive drugs. Shy-Dragers disease often presents with acute hypotension. If dad was to go off of sinemet cold turkey, I would think this would be a very bad thing. Shy-Dragers is also often dopamine unresponsive. The pyridostigmine is an acetylcholine esterase inhibitor, which are about the only class of drugs considered useful in dementia control, especially given to Alzheimer's patients, as there are no drugs proven useful in stopping the symptoms of Alzheimer's. Maybe dad is going down because the l- dopa isn't doing anything for him, but is making his hypotension worse. The others advise to taper down is correct, but I would get a skilled neuro's opinion on this. My fear is that a quick withdrawal from dopa would see a hypertensive event inevitable, with potential consequences.
As far as your dad being " delusional and obstinate" these are, unfortunately problems that only he can be convinced are part of his current disease state and you can only hope that he can accept this an put his faith in your words to him that he is not seeing things clearly. This kind of ideation is very common among " the terminally medicated", and can destroy life long relationships.