Two thoughts (from a non-American, so maybe that’s impacting my views on this?):
I can see an argument for permitting law-abiding civilians to bear arms in public, including in Church.
I am honestly concerned to hear you say this:
Why is your wife so afraid of this? Does she know a fellow parishioner who she suspects to be violent? Has she suffered violent abuse or trauma in the past? Has a church shooting recently occurred in your city?
Yes, I know the news media broadcasts stories about mass shooting events, including in churches, and these are real. At the same time, unless you live in (e.g.) the Middle East, they are rare. Is there a concrete reason you fear that your life is at risk inside your particular church building?
I don’t mean to dismiss your fears. At the same time, it’s hard for me to relate, and I’m having a hard time following what you’re saying. I live in a large city, I’m a woman who lives alone, travels on public transit, has to walk through sketchy areas of town, and (obviously) I go to Mass every Sunday, as well as all sorts of places. And I’ve never held a gun in my life. And I’m not afraid.
Sure, someone could technically kill me… but I could also die of a brain aneurysm, or heart attack, or a car could smash into the bus. All these risks are just statistically so low (at least where I live: Canada), that I just sort of… live without fear. After all, I’m right with the Lord. What do I have to fear from death anyway? He’s already conquered it.
So basically I guess I’m saying, I wouldn’t mind a church letting you carry your gun if it helps you feel more secure. But I’m sincerely concerned for you that you (and your wife) seem to live in such a state of fear about this, and I would honestly suggest that you take that to prayer with God, because as Catholics we’re not supposed to be this afraid of dying. Jesus commands us not to be anxious. Maybe that’s a scripture you might spend some time with? Matthew 6:27
“And which of you by being anxious can add a single hour to his span of life?” – Jesus