I'm curious about how she understands you and guns in general.
Does she think that you are obsessed with them? I've been obsessed with things in the past; the wife takes an instant dislike to what ever that thing is.
Do you have an attitude about guns that she dislikes?
Do your discussions leave her frustrated?
I ask these few, basic questions to cause you to consider if there is a prior disconnect between you and your best friend that needs addressed before you resolve the CC issue.
Maybe she doesnt really understand your fuller role as protector or maybe sh thinks you act like Rambo. I dunno. But many times it's about the perception rather than the substance.
I remember when my family were visiting a national cemetary and guns were not permitted; she was slightly shocked o realizing I was pocket carrying. Over time I showed her that I took gun safety and training very seriously.
I wish you wisdom. List her concerns and ponder replies to put her concerns to rest. Because in the end she needs to know that you are going to CC.