Should we monitor my mom’s cigarette smoking?

If you are with her to make sure she is safe with her smoking, I don't disagree with what you are doing. I would not encourage smoking too much, though. First, it isn't good for her lungs. Second, she may have to go into a facility ultimately that doesn't allow smoking. It seems to me that quitting a small habit would be easier than a bigger one. (I don't know if this is true, though.)

At this point I wouldn't be too concerned with the health issues.

What is your role in Mom's care? If Dad is her primary caregiver, I think sneaking behind his back and undermining his authority may not be in his or your mother's best interest. Perhaps that isn't the case -- but give it some thought.

Do the cigarettes make her happy? Would something else make her equally happy? Could you discuss your point of view with Dad, and perhaps come up with a compromise, or at least understand each other's views. What are Dad's reasons for wanting to limit the smoking?

As Jessie says, if she eventually need to be in a care center, she may not be allowed to smoke at all. I'm not sure whether that is an argument in favor of letting her smoke all she wants when she can, or an argument in favor of cutting down to reduce withdrawal problems if she has to stop.

I don't see clear-cut answers here about the smoking, but I wish you and Dad could be more open with each other.

There is something else that I missed. If her dementia is vascular dementia, the cigarettes could hasten further decline through their effect on the heart and blood vessels. If she has vascular dementia, I think your father has the best plan.

Thank you for your input. She has no desire to quit smoking. Currently she has been living at a facility, but comes to visit for two nights a week. She can’t smoke while she is there, but when she comes home she wants to smoke. I tried to avoid her from smoking when she first came home for a visit. The current plan is for her to move back home by thanksgiving. There is no fear of her starting a fire because she is unable to light a lighter. So, me or my dad must light her cigarette for her. My main concern is her nicotine fits. I don’t think that can be good for the body. Me and my dad are her primary caregivers when she is home.
Dave