I am in a similar boat of convincing my wife that I am not one of the doomsday preppers she sees on TV. Over the past two years we have suffered a few prolonged outages thanks to winter storms and hurricanes.
I have flat out told her that this is what I plan to do, and that I am not nuts for doing it. I am taking steps to insure that my wife and 3 boys are warm and fed in the event of a prolonged outage or other such event. To that end I have:
1. Provided for defense. I've got rifles and a good bit of ammo. No need to say more.
2. Water. I have about 75 gallons of drinking water in the 5 gallon bottles. This is for drinking and cooking. I also have several 5 gallon bottles of water (still potable but not sealed spring) that is used for cleaning, hygiene, and toilet flushing. If need be, I live near a lake, that water is easily replaceable and that water can be purified if the going gets REAL tough.
3. Food. My family is young and single income at the moment, and we have 3 young boys. There is no such thing as a food surplus in this house. Anyway, whenever I do the grocery shopping I always make a point of buying a few cans of non perishables, such as vegetables, spam, fruit, pastas, etc. I'll never have the bunker full of food, but as I explain to my wife, I want to keep enough food in the house that we can go it for a few weeks if need be. I'd like to have 3 months, but it is a process....
4. Heat. The home is heated with a forced air, oil fired system. I have a generator that can fire the furnace in the event of an outage. As back up, and I have had to do this before, I have moved everyone into the basement and heated the basement with a ventless propane heater supplied with a 100lb propane tank. Even with a ventless heater one should always use a carbon monoxide detector. Moving everyone into the basement lets me avoid having to heat the whole house in the winter, and during the summer, it stays cool down there anyway.
It isn't perfect, but it is a start.