With your needs it seems unrealistic to think you can bug out on foot and have the supplies you would need. Just the food for 5-people for any length of time (with only 2 of them able to carry any kind of pack) would be more then reasonable to carry.
Better to plan on a car or SUV as part of your bug out plan.
Always have a supply of fuel on hand so you won’t have to worry about it when the emergency comes. With fuel stabilizer you can store gas for a few years and still expect it to work right.
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You can run, but you'll only die tired.