My father is a smoker and has been smoking since he was 11 (39 years!)... he has agreed to give up for the sake of being able to have a 'hands on' relationship with our bub. He agrees and understands that even if you do wash your hands you are still carrying contaminants on your clothes, in your hair, on your face etc after smoking.
While we didn't give him an ultimatum we did tell him that it would be an issue for us, as neither of us are smokers. In hindsight he knows that it was the motivation he needed to make a decision that will be of benefit to him.

Good luck, and I hope your Mum understands and sees the positives that can come out of this