The lack of sleep for parents during a camp out has always been an issue. Put the little ones in a folding play pen so they can not escape. You will sleep better. For family camping you can't beat a cot.

I really think you revert back to a more normal/natural sleep pattern when in the woods. Watch any animal at night and you will see periods where they are alert and then doze back off. I think this slight awakening to check the surroundings is quite natural and definitely leads to better survival success. Zombies only come at night you know.