http://www.jpfo.org/filegen-n-z/ragingagainstselfdefense.htm
If that hasn't already been posted, it may be good advice.
I REALLY feel for you.
In a way, honesty is most important, but I think your wife has deluded your daughters. I think she is delusional. There is nothing wrong with saying "I don't want to carry a gun," but no one in their right mind wants to keep a law-abiding citizen from carrying a gun. Getting emotional about it is a real sign of some type of thought disturbance.
Here are a few strategies I might employ:
-Talk through their feelings about self-defense:
"You: What would you do if someone tried to harm our daughter in front of you?"
Your wife: I would attempt to prevent them. [Hopefully!]
You: How would you do that?
Your wife: I would scratch, claw, bite, do whatever I had to do.
You: What if that wasn't enough? Hypothetically speaking, would you be willing to learn a martial art if you knew this was going to happen?
Your wife: I would do whatever it takes to protect my daughter.
You: Would you use a hammer, or a knife if it was around at the time?
Your wife: Yes, of course, I'd do anything.
You: Well, I realize that you want to protect our daughter but do not want to carry a handgun. I think that my choice to carry a handgun is wise because it is the best form of protection that exists for people going about their daily business. I conceal, so no one ever has to know. If you'd prefer, we can avoid talking about it. But my choice to use a gun in defense is no different from learning a deadly martial art or using a tool of opportunity.
You don't want to play the "What if...someone tried..." game too much, because it is disturbing to "pacifists" to think that their bubble could be popped, but it is a useful option.
-Go into counseling. Choose a fair counselor, but one who isn't rabid anti-gun. Attempt to resolve this and prove you are open to suggestions. The more open, and less vocal, you are, the greater chances are your wife will follow suit.
-Realize that your choice to carry IS a personal choice. Do you ask your bro about his sexual habits, his diet, and other things you (or someone) might disapprove of and then judge him based on it? Chances are your choice to carry will never affect him at all, and if so only indirectly. The honesty issue with your wife is tougher, but ultimately I think you will be forced to conclude that she is delusional about that matter; brainwashed, if you prefer. You love her, but if she suddenly started demanding something else unreasonable, like that you stop wearing your seatbelt while driving, would you acquiesce? Doubtful. This safety choice is personal. A temporary fix could be to resolve it on a personal basis with this point of view, while promising yourself you will try your damnedest to resolve it with her through the above venues.
-Don't let anyone, especially not your bro or your wife, convince you that you are being unreasonable or that this is a "marginal" issue compared to your marriage as a whole. This kind of thing can really drive a wedge, but don't let that convince you you're wrong. Vehemence on the part of the dissident doesn't equal righteousness...
Good luck, please try to reply to my suggestions if you can. I'm interested to hear your thoughts.