Children count on their parents to make good decisions and lead by example especially in high pressure situations. I am sure that you have been plenty hard on your self and mistakes and accidents do happen. How was this an accident? Click the safety back on! Having read your story and deliberating on whether or not to post I have to say something because it is obvious that people on this site just want to be nice... or possibbly don't recognize this as a lapse of ethics. Let me backup..
I have three children and have had them take 8 cows and 1 bull over the years. They haven't killed an elk every hunt. I have been in your exact position... and thought what you were thinking at that same moment. IT IS TOUGH! Success comes in so many forms and for our children it shouldn't be about just getting an animal at any cost. There are other opportunities. I look on this site and see the kids surrounded by family, friends and the great outdoors which is the way it should be...but it should be without these type of stories. God Bless you,your family and all of your future hunts.