Hi! When we use the phrase "should have" it means that a course of action would have happened if something hadn't gotten in the way and prevented it from following through. Here is a sentence to show you what I mean...
" I should have been to work at 9 AM but I had car trouble!"
I am saying that the only thing that stopped me from being at work at a certain time was car trouble. That's where I had to be on this day at 9 AM.
When we use the phrase "could have" it means that there is a possibility that something could happen but it's not concrete. It could be left up to a person's choice or it may be left up to chance and fate but it doesn't have to happen. See how this goes in the following sentence...
" I could have come to the morning meeting at work but it wasn't mandatory, so I decided to get some paperwork done instead."
So, here there is really nothing stopping the speaker from attending that morning meeting (Like a car accident on the way to work.) they just chose not to go because they weren't required to.
Now the interesting thing about the burglary victim's statement is that we don't know the burglar's intent. Were they just going to rob the couple and used weapons to scare them into cooperating or were they more like serial killers where the only reason to break in was to murder someone? I don't have that information. I assume the victim is really frightened and emotion makes him feel that he and his wife were in danger of being killed so maybe should have is appropriate in the emotion of the moment if the real motive isn't known. The other thing is when he said his kids "could have" been dead. What does that mean? Where they not at home that night?
So, "should have" (Something got in the way of fate) or "could have" (There are options on what might take place). I encourage you to look up the definitions of "should" and "could" in the dictionary and think about how you use each word in English and how you similarly express yourself in your native language.
