...should I assume our whole family will be leaving together, thus eliminating the need to duplicate items?

You've already been given great direction to decide what a BoB needs. I'll give my opinion on this one part of your question: There are 2 kinds of items to consider in regards to this question.

There is "Personal Gear" that each person needs to carry for themselves. Examples: Sleeping bag, mess gear, toilet paper, canteens/water, knife, flashlite/headlamp, personal FAK, etc.

Then there is "Community Gear": this is gear that the entire group will have use for, but this gear won't be needed by each person, at the same time. Examples: Tent half or parts, axe, AM/FM/TV/SW radio receiver, fire grill, etc.