In my mind I'm seeing myself opening the door and immediately shooting back into cover. He doesn't see me and all he sees is an empty doorway. From that cover I line up the perfect shot and I take it. That is a 1 in a zillion chance. But, for me, I feel a little more prone to take the shot first if I have one because if I can get that perfect shot I don't want to waste it.. especially if I can't account for my other family members or think one or all of them are wounded. That shot may never come around again and the lives of my family are on the line.
In my minds eye I'm seeing a hardened expression with blood lust in his eyes but, of course, that may not be the case. He may be more than happy to put my child down and leave if given the option and you are very right that that option should be given to him.
"Put her down now and you can walk out of here!"
I don't think I would say, "Put her down or I'll kill you." That kind of threat is going to make him NOT want to put her down. He has a human shield for a reason and he's not going to give it up if he thinks he's in danger of being killed. I think threatening death right off the bat amps things up.
I read something not too long ago (not sure where.. I'll have to look) that many criminals resort to violence only when they feel like they cannot escape and it is their only option as a means of escape.
In desperation at hearing me come home he might have grabbed my daughter not really knowing his intent. Now that I'm there and threatening to kill him he very well may start thinking violence to her or another family member may be his only way out. But if I get there and say, "Hey, put her down and you can walk out of here." It might be exactly what he does because he doesn't feel cornered or threatened.