Wow. Ok so, let me say that you have a shit-ton of willpower in keeping the quit. Some smoke more when stressed, some smoke more when happy (like I did). I imagine most smoke more when stressed.
Sounds like his falls are more of a non-event.
About them refusing help - Yes, aging parents are stubborn as an old mule. I guess no one wants to face up to the day that they are no longer on shape to take care of themselves.
I am not in much position to give "advice" but sooner or later they will end up in the hospital and you might have to secretly get social services involved, find out what options there are, etc. Home hospice may be the answer. When my mom was to a point where she just could not live on her own due to failing health, one time I had to call an ambulance because doing it myself was just beyond my ability. I am no medical professional.
But with home hospice, a nurse comes by the house to make sure things are taken care of, gives meds, brings whatever needed medical equipment, etc.
And if you are wondering, yes, my mom died in her own home when her time came.
Just call one of the home hospice places and find out what requirements are. It is not a fun decision to have to make but when our parents are older, WE become the care takers. Our parents sure as hell are not going to say, "Oh great! Oh yes, I am thrilled about the prospect of making final decisions!"
No, it is more like, "I don't want to think about it right now".
This might seem overwhelming but you don't have to do this on your own, in fact you probably can't do it on your own.
BTW, I asked one member on this forum to contact you about caring for aging parents, but I do not know if this person is in a position to right now or not. If they do, don't be surprised or anything.