Have a listen to this podcast about safety,
http://cdn1.libsyn.com/jmiller/140_tfp_ ... ba3f8adf22
or you can navigate to our audio podcast page, Edpisode 140.
Basically, pre-flight planning/safety is broken down into these categories-
I would systematically work through each one of these and explain the process that occurs before each and every flight. If you want statistics, go to AOPA's site.
I would also ask if this is about flying or just fear about the kids being in a situation she doesn't know. I know you say she won't warm up to GA, but perhaps sharing information, ie podcasts/events, even a flight? might help?