I hate to be that guy, but. . .
First of all, I'm extremely lucky in that my wife not only supports my carrying of a handgun, but also carries one herself. I've known for a very long time how lucky I am. We used to compete in USPSA and IDPA matches around the midwest practically every weekend, and you wouldn't believe how many guys would tell me how they wished their wives were like mine.
I had to put that in there to explain where I'm coming from so you'd have an understanding of my circumstances. No, I am not walking in your shoes. I know I got lucky that my wife and I have a LOT in common. In fact, before I married her, I made absolute sure of 100% compatibility in a few areas: Politics, sex, and religion (guns fall under all three, as far as I'm concerned). We've been able to sustain a happy and productive marriage for 22 years, so far.
I apologize if this sounds harsh, it's not intended to be so. It's intended to be as objective as possible.
This problem you're facing is one that is deeper than most people would like to admit. This shows a fundamental difference in beliefs held by you and your wife. Moreover, it shows a deeply-held distrust of you. You are, presumably, an adult and capable of making adult decisions. Your decision to carry a firearm should be respected by her, even if she disagrees with it.
She is exhibiting some fear. I'm not sure how deeply you've delved into her reasoning behind it, but there's something there that gives her an unreasoning fear and distrust. You can try to root it out of her.
However, and I realize this is an archaic concept, but. . .I am a man. I am an individual. I am, so far, a free man. I carry a handgun for several reasons, only one of which is to protect myself and my family from harm. I take that decision very seriously and no one is going to convince me to do otherwise. Yes, I guess I'm violating the forum rules by stating that I carry a handgun where people tell me not to. No one. . .NO ONE is going to tell me that they will only trust me if I'm disarmed. There are very few places I will go without a firearm, but I willingly go to those places with the understanding that I am taking chances when I go there unarmed (i.e., a courthouse and the airport).
I will protect my children. I will protect my wife and I will protect myself, despite what their wishes are. To me, that is the duty of a father and a husband. I carry my handgun(s) to my friends' homes. If they tell me that don't trust me unless I'm disarmed by asking me to leave a gun outside or at home, then I will not visit them, be damned the social stigma. When I carry a handgun into a friend's home, I am not telling them that I don't trust them. Rather I am telling them that I will protect them as if they were my own.
I have a difficult time respecting any man who refuses to protect his family. If he's alone, childless and unmarried, then it's his decision if he wishes to brave the dangers of the world unarmed. However, if he has a significant other and/or kids, it is his DUTY to protect them, even if he finds it distasteful.
But if anyone has a partner who is so diametrically opposed to him or her to protect not only themselves, but their partner and their children. . .there are going to be greater problems down the road. Especially if she expects you to willfully surrender your most basic human right (to protect yourself) simply because she has an irrational fear. You're caught in a bad situation. Give in, and you run the risk of her not respecting you, or your decisions. Don't give in and she can make life hell for you.
I don't envy you your situation one little bit. And yes, I do thank the heavens that I found the woman I did. I will admit, despite an expectation of drawing quite a few posters' ire, that I don't understand how a relationship with such a fundamental difference can be expected to last (and yes, I have had relationships that weren't as compatible. . .and they didn't last). Please note that I am not telling you to go find another wife. Another part of a marriage is finding ways around situations such as this. I just find it . . .perplexing, that's all.