i really also encourage you to get a full alzheimer's workup for your Mom. all alzheimer's is dementia but not all dementias are alzheimer's. beside which, lots of other things look like what people think of as alzheimer's. the work-up helps to identify some of those other things. falling is not a usual part of alzheimer's, so she is very likely to have other important health issues to account for that and possibly even to account for the appearance of dementia. Medicare pays the whole cost of the work-up.
i must say, i hate to hear she's driving still. i have a useful motto for that: "families don't let family members drive demented". The accident rate is huge, about 6 in ten in the months before finally a family intervenes, including death-causing accidents. and, i hate to add this, but it's a liability issue for the family.
no-one wants to think they aren't managing their life, especially if they aren't. i've found that it may work better if you take it on yourself, as in, "Mom, I know you don't feel you want extra help, but i love you a lot and i worry about you so much. i know i shouldn't, but i do and that's why...blah blah blah." There's no accusation in that and you own your feelings and it's hard for a person with dementia to argue their way round it.
i also suggest the family conference -- a sort of care intervention. and since your Mom is both falling and smoking (though presumably not at the same time), that the danger elemtn in her house is pretty high. i endorse ann's suggestion that you bring in a helper, hang out together with your Mom and the helper until some bonding is happening and then let it be. it'll probably work quite well after that.
nothing is perfect, but planning helps. and i respectfully suggest to you that your mother needs help now. if you're waiting for the time she says, "Oh honey, you're right, it's time for me to have help. please find me someone..." that's likely to be the 12th of never, to be honest. if you see something wrong now, then now is when your intervention is needed.
Go for doing the right thing for her needs, not the right thing for her to be pleased with you. I know that you'll feel better when you know she's being helped as much she needs, even if she complains to you about it. that's when you just say, "Uh-huh, I know, Mom" and you'll know you took care of what was needed. she'll probably come around on it when she likes her helper.
go to a local caregiver support group -- you'll learn lots and you'll get the support for doing the right thing. you may possibly even find a good help person through that.
From Frena Gray-Davidson" author of "The Alzheimer's Sourcebook" and "Alzheimer's 911."