I think it has a lot to do with age. If your mom is 35 to 70, it could work, older then that doubtful.
My mom (85) has lost a part of a lung to cancer, she can't take a deep breath, she coughs all the time..but to her E-cigs are stupid. She took a puff and coughed..that was it. She prefers to smoke, all day, even though she can hardly work a lighter anymore. It's what she knows and what she wants.
It's also mindset. Your mom knows how ill she is, if that alone doesn't motivate her I wonder if an E-cig will do it.
I would have her look at pictures or a video and then ask if she thinks she might like to join the revolution against high cigarette taxes? Believe me telling her she has to do it for herself, the grandkids/future g'kids and you is too much pressure!
One more thing, is she an independant woman, can she handle all the charging, cart filling ect.? It's a lot of fiddly kind of work. I am 58 and love all the fiddly stuff, it keeps me busy.
I meant to add, she will probably want regular cigarettes for a while, she may quit, may not but if you can get her to slow down on cigarettes, what's the harm? Don't forget to make it fun, flavors and pretty colored e-cigs. At least at first..then she may want a screwdriver!