For a story, you want conflict that gets resolved, either in a positive or negative way.
You want a beginning, such as: See this ordinary family. Look at their normal routine.
Then there needs to be a middle with the introduction of conflict (Pick one point of view. Maybe the mother. You can have her leave the message for the school on her Cell Phone with a dying battery instead of chipmunks chewing on the wires. You can give us the suspense of her looking for her daughter, wondering where she is, running into a friend of the daughter who asked why she wasn’t at school, this kind of thing.
That way when the killer attacks the mother, you have a sense of suspense.
Then you have to have an ending, perhaps you could write it as though the father had a fighting chance, giving your readers an opportunity to feel like the nice family will win before the killer takes him out.

One last thing: Do a little research. Few people do things like this for no reason. The killer being “Crazy in the head” is not sufficient, especially for a jaded modern audience. He needs a reason why he’s acting this way. Did he have a motive for taking out this particular family. Why was he obsessed with three-person families. You said something about losing a family; typically this kind of psychotic break would require some kind of childhood trauma first, before he lost his wife and child. Give us a bit of what is going on in his “crazy” head, and not as a little postscript. Do a little bit of research on serial killers; there’s plenty on the internet.

I also recommend joining a writer’s workshop group if you want to write stories. There’s a high demand for thrillers, mysteries, and the like, but you have a lot of work to do before you’re ready to be published.