Curare, it sounds like you have your hands full, and I sympathise. For the most part it would be difficult, or counterproductive for me to offer advise, you know best your own situation. My wife (of six years, and two kids) is a former MP, college educated and still "has her moments" when ... shall we say she channels Oprah. As previously noted, facts do not trump emotion. And when the names, like "mentally ill" start flying, it is hard to stay to the High Road, but stick to it.
The fact that I have "protection" along with me most of the time has nothing to do with the circles permanatly engraved in my old college wallets. It was like that when we met, was a constant factor in our courtship. When we started getting serious, I showed her the contents of my safe and asked if she could "Deal with this", as it was not about to change.
We discussed the reality of the sitation, that "I go or the guns go" had only one conclusion (Not that it has not been uttered when emotions/hormones are high), came to agreeable terms and for the most part, this has worked out well.
Speaking as a former (still dabbling) LEO, I applaud your wish to CCW, especially in the light of the events in Omaha. Getting the responsible citizens aware and involved may be the last hope we have as a nation vis-a-vis the domestic problems we face.
Hold your ground, but listen attentively to her concerns. This is most likely a power issue to her, as has been said. Explain your desire to keep her and yourself safe, establish were the weapon will be kept when you are not wearing it (those four-finger push button lockers are great, and inexpensive).
Speaking as a fellow buckeye, PM me, if you wish. if we are local, let's hit the range together.