As another reply said already your biggest worry will be confiscation of your supplies by others who think they deserve them more than you. I move bugging out a notch higher on the priority list. Are your children old enough to get into camping and boy/girl scouts? I would get them their own camping gear and make a place to store it all and start taking them out for a weekend of camping every so often. Make a couple surprise camping trips where everyone gets home from work/school and you grab your backpacks and gear and go. Then if something happens you grab your camping geat and bug out. I'm not saying hide whatever is happening or try to lie about it or anything like that but when something does happen and you say wife/kids we need to leave grab your camping gear they will have something familiar to them which will help calm the situation.
I have a small propane grill that we take to family reunions and such that everyone calls a camp grill because it is similar to the old coleman camp stoves. it was a replacement for our old big grill which took up too much garage space. So I pull out my normal grill and cook out through the summer and now have a means of cooking if we have no power and is portable if we have to bug out somewhere. Items like this are useful without being too "survivalist".