I believe that if put in this horrific situation I would have to forgive not for the murderer because they deserve it but because I deserve it , the family and I would deserve to be allowed to live our lives and move on and I think you can only do that if you forgive . However I have never been put in that situation (thankfully) so I don't actually know how I would react.
To put it as simply as possible, if the murderer had no other choice and it was an act of self defense, kill or be killed, I would be able to forgive the murderer.
I'm sure there are other circumstances under which I'd be able to forgive the murderer, but it does rely entirely on circumstance.
I don't think I could ever forgive someone for killing anyone I love, whether or not they were my family. But especially my family because I see that as not only a horrible action taken against the family member that was murdered but an attack on the family as a whole. The murderer not only killed someone, but severed a proverbial limb of the psyche of the family member's of the victim. That person is now abruptly gone from their lives and will never be there again, no time to say goodbye, no nothing. I would never forgive someone for doing that to me or my family. (This opinion is only relevant if the family member was not killed in self-defense and was not the aggressor.)