I never said you should not warn your family, that part is entirely made up by you. It is not 'kill or abandon everyone to inevitable doom.'
Your choices will include 'flee and abandon your family to their deaths' which fails to be illegal but should be
Your choices will include 'blow up the house with dynamite'
Your choices will include 'try to win a shoot out in the living room'
Your choices will include 'try to get the family to safety while also trying to gain a position where if conflict becomes inevitable you have the upper hand'
Your choices in such a situation also includes running up to the burglar screaming some aztec curses wielding a spear
The choice that is legal is of course 'try to get the family to safety' etc. Happens to be the choice with the best chance for survival for your family of.. 5 as well
Edit:
The key here is that in any situation if deaths are not unavoidable they should be avoided. Killing people just because you are offended you might loose a lamp is such a waste, lamps can be replaced.. even if they are designed by PH
Having fleeing not a choice is btw a horrible attitude that may in some theoretic situations get your kids murdered. You may want to reconsider limiting your choices even in a country where gunning people down left and right is an option. By the time the burglars have killed you they are as i understand it in some states guilty of first degree murder since they committed the killing in the process of a crime. That in itself escalates the situation