You have the right to make that call if you have power of attorney. I worked in a nursing facility for 16 years before going to a hospital and you are right I used to give meds. Most of the time they do give these meds hoping it will put these people to sleep so they don't have to mess with them which I totally disagree with. I had the right as a med nurse to use my own judgement on giving meds and I did. But not everone does and yes if he has tylenol ordered they should have tried that first before giving him a narcotic. If I was that concerned I would discuss this with the head of nursing and request he not get this medication and discuss this with his doctor. You do have that right.
Like your father, my sister had many complications after her stroke. When she got transferred to the subacute facility, we had to get nasty with some of the people there. It was a matter of getting the head of patient advocacy involved. If your dads situation is anything like my sisters, he cannot ask for the help himself nor is he completely aware of what is going on, you need to be his voice. Keep a journal of all the medication that is given along with the side effects that you notice. This record keeping will help in the long run. Don't be afraid to speak up and question things. The more involved you are, the better he will be taken care of. To most of them, this is just another patient passing through.
My prayers are with you.