When I first started concealed carrying, a while ago, I just started carrying it concealed and didn't tell anyone. Not even my wife. IF you are carrying it "Properly Concealed", then not even your wife should know that you are carrying. Now, if you're telling her, or letting her see you get all "geared up" to leave the house, then that could cause her to take notice.
I'm not saying how to address your wife. And personally, you shouldn't be asking anyone here for advice. You have a personal relationship with your wife, and you're the one who has to live and deal with her and that relationship. Obviously, an suggestion of: "You need to discuss it with her" is the right advice, and also pretty obvious. Any advice beyond that shouldn't be followed. This is something only you and she can figure out the right way.
For those who haven't gotten to this point yet in getting your CCW permit and are starting carrying, I believe in the concept of it's better to ask forgiveness than permission. When I first started carrying, and got my permit, I didn't tell my wife I received my permit. She knew I applied for one, but I left the conversation at that. I never told her when I got it. I already knew where I WOULDN'T carry, (That's MY choice, so don't question it), I also knew where I COULDN'T carry. So when I was preparing to leave the house, and I was going to carry, I armed myself inconspicuously. I didn't let her see me carrying. After a few months, she finally asked me: "Why did you apply and pay for a CCW permit if you aren't going to carry a gun". I simply said: "I've been carrying a gun outside of the house for about 3 months". She looked at me puzzled and said: "I never saw you with a gun". I said: "That's the way it's suppose to be". Now, it's never even a discussion. Then again, I'm not one for "bragging" about what I'm carrying. Which is common among some of those who open carry. They are quite obvious that they want people to see them, the gun, and their posture. But that's a different topic. Point is; if you're going to mention it to your wife, kids, neighbors, etc... then they are going to be away of it. If you don't mention it, and they ask later, and you say you have been carrying and currently are, they are much more accepted of it. Because it obviously isn't causing the potential problem they THOUGHT it could.