You'll undoubtedly get tons of replies and opinions, but here's mine -- from one that hasn't handled a shotgun in decades:
Determine how quickly you can load said shotgun in total darkness or chaos, and then make the determination. If you're secure that you can make it fire ready in 3 seconds, you might feel better about acceding to family fears. If not, then take wifey/daughter out for some trap shooting -- they'll discover a great new sport, and come to love your new household addition.
That’s very similar to what the gun store owner told me. Thanks.