Should I let a stranger in my apartment if it is an emergency and they have kids?

You have no obligation to let people into your home and in my opinion you SHOULDN'T. It's not safe, it's not smart. Just in case something crazy like this ever happens again, check through the peephole in your door before opening it, and always make sure the door is chained before opening it so that noone can force their way in. If you don't have a chain, install one.