In New Jersey even B-B guns have to be licensed, so I wonder how easy it would be for her to get a license. It's great the lady is perhaps seeing the light, but someone with a mindset that she's had all these years, which was probably anti gun, may not help at all if she does get a gun regardless of the kind. A son should know his mother well enough to know if she's capable of even using it, let alone handle one safely. If she's not that type then she should forgeddaboudit.
Her age is not ancient, but it's a little late in life to start handling guns. I know many will disagree, but then again I'm older and am very familiar with older women. Many older men couldn't suddenly later in life safely keep, or use a gun under pressure either. I have a feeling this may just be an over reaction to something she's seen, or has been hearing on the news. I'd just tell her to be more aware of security and not to worry. If her son thinks she can handle using a gun then help her get one.
It's a pity how these politicians are stressing people out for political gains, which because of their greed really means power and money.