Plan A should always be to dig in. You leave only when your static preperations and shelter probably (no possibly) will be or have been compromised. With little kids, this is more critical just becuase they can't take the amount of exposure (weather-wise) and abuse that an adult can.

As others have said, it's you, your wife, bug out gear, and no offense, two pieces of squirmy luggage. I wouldn't be thinking bags. Kid carriers with some cargo capacity, and a something like a game cart or cargo sledge to carry the bulk of the gear. I wouldn't count on your eldest to be walking very far, certainly not more than five miles a day, unless he's used to it.

And honestly, I'd put terrorism near the bottom of your priority list.