Is your mom overweight by chance? If she is, you should definitely talk her into doing it. Tell her that if she still feels it's unhealthy after two weeks, that you'll just go it alone without her support. I was 18 when I first started Atkins, and I can't really remember how I brought it up to my mom, but she did some research and we went on it together. My mom was pretty overweight at the time, and the next morning she had dropped 8 pounds (I know this isn't typical and mostly water weight, but it's still more loss than if she had been doing low-cal or even just starving herself). Needless to say, she was sold. And even if your mom isn't overweight, she can still get a lot out of low-carbing.

Like what was mentioned before, she's probably just listening to all the nay-sayers out there...they assume that we just eat piles of bacon and mayo out of the jar. I know some people do that, but I eat WAAAAAY better when I'm on Atkins than otherwise..I eat lean meats cooked in healthy oils, and a ton more vegetables than I normally would. In fact, I was at my all time heaviest when I was a vegetarian. To end my rant, I'll just say that most reputable sources will say that this is a completely safe and effective way to lose weight. We managed to evolve into homo sapiens without one single bagel.