If the choice presented is unacceptable, take the third option!
My family dying and taking a shot that I believe has a greater chance of hitting an innocent than the attacker are both poor options. Given the scenario (only poor options available, and the realization of the choice), I would not want to fire. In real life, I don't know what I would do. The intricacies of the real world complicate things...
On the other hand, the complex world provides more choices!
Certain injury of loved ones/self versus probable injury of innocents are not the only options. This is why a firearm isn't your only weapon. If I cannot fire, I'm going to plan B (or C or D or E etc...) I usually carry several things that could be used as weapons, if need be. I also bring me
along quite frequently. Sure, my chances of protecting a loved one are not as good as using a firearm, in the hypothetical, but the risk of harming an innocent is also lower. I'll take the 30% chance of success and 10% risk to innocents over the 80% chance of success and 80% risk to innocents or the 0% chance of success. It's still a poor option, but I think it is better than the others.
This is T&T, how can we exclude options other than "all or nothing with a firearm?"