She's a mom, and she's always going to worry about her baby. It's not an easy sell, maybe even impossible depending on how against guns she is. My mother was very anti-gun when she was younger. She supported a person's right to own one and believed Big Brother should stay away from a citizen's right to own one, but she wanted nothing to do with a gun, personally.
She did eventually come around and now owns 3. There was no specific catalyst that converted her, it was just a lot of things over a period of time. I'd say it began with reading NRA material. Learning that there's more to owning a gun than simply "gettin all liquored up and goin shootin!!" And she may even subscribe to the "If you own a gun, you're probably going to shoot one of your own family members instead of an attacker" (ugh, I hate that!). Get some reading material, and discuss it with her. She may not convert, but she may be a bit more comfortable.