I think the issue is that as The Campbells are more than one person any apostrophe should be The Campbells' home/cat etc.
Hair splitting that hasn't helped the debacle at all though.
Boxtops, you posted:
"you could say THE CAMPBELL'S NEW HOME"
which is virtually impossible usage as you are turning Campbell into a singular noun. It would be: the Campbells' new home.