A shotgun is a great home defense weapon IMHO. However, I would ask how big is your mom? I ask because a 12ga has a bit of kick for the smaller people. I'm only 5'6" but I weigh 165lbs so the 12ga is great for me. My girly however (who has never actually shot a shotgun) is 5'2" at 105lbs so a 12ga may be a bit big for her. Pending on her size there is always the 20ga and the 410. If your going to go with a 410 though I would maybe consider getting something like this Taurus .45/410ga revolver that can be loaded with both .45 long colt and 410 rounds. 5 rounds. Very lightweight. But you can't go wrong with a scattergun in my opinion.
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