If someone was murdered by a killer in a house, 1) Would the family definitely move? 2) If no, what reasons would there be for not moving, beyond financial? 3) If yes, what reasons would there be for moving back, again beyond financial?
Did the murder take place right in front of the family? Is the house in an obvious slum and/or reportedly violent neighborhood? If the murder was many years ago and there's simply a bad feeling surrounding the house, there'd be no reason not to move in or continue living there. If the murderer was, say, a family member or friend, yeah I'd get out of there as soon as possible to avoid the media and other backwash that will occur when you're associated with someone who ended another person's life. Money is a pretty good motivator for moving somewhere. If I can afford a house, for example, I'll buy a house and take with it all of the advantages and disadvantages that come with it. If it's more cost effective to live in a rent controlled dive then so be it. It all depends on the needs of the individual. If you moving into the house would provide a presence enough to keep a relative from taking it from an older person or your grandmother while she's int he hospital, that could be a legitimate motive.
It depends on the connection the family has to the home. Even if a terrible tragedy occurred, some people would not want to leave the home they have spent decades in. I've seen (in novels) it go both ways.
How likely is it to get killed there? I mean if it's a ghetto with a very high crime rate, you might want to move before anyone is killed. But if it's a nice, suburban neighborhood with a more or less non-existing crime rate, I would ask how related the murder is to the family. If it was a random murder and the killer was caught, I wouldn't have a problem living there. It's not likely someone else will finish the job on the family, after all. But if the murder targeted my family on purpose, what makes me think the killer won't come after my family even if we move?
If someone was murdered in my home I would want to move! There would be no way I could sleep in that house again! Moving back would be hard, but I guess if the other family members wanted to move back I would think about it and only if the murderer was dead or in prison.
there's no one-size-fits-all answer to your questions... it all depends on your story and your characters... so only you, as their creator, can supply the answers...
Part of the plot of your book could be the family making an attempt to live in the house, but having to confront shadowy memories until they eventually make the decision to move. I don't know if you saw the movie about the two single people who ended up having to take care of their brother/sister's child after they died in a car accident, but that part of the movie (when they decided to take away all of the reminders and redecorate to fit their new family) was actually quite poignant.
