"So there would be no problem if your family got caught in a cross-fire on-board this aircraft?"
The short answer is, NO.
The long answer is:
1--I have taught my children the following: "They that can give up essential liberty to obtain a little temporary safety, deserve neither liberty or safety." Benjamin Franklin - 1759"
So, they would be one of the armed passengers and ready and willing to defend themselves.
2--Better to die in a proactive defense of your life, others lives, and others property than to die as herded sheep in the back of an aircraft flown into a skyscraper.