If the Campbells is the name of the family, then the plural (all the Campbells)is just CAMPBELLS. if you put the apostrophe in, you could say THE CAMPBELL'S NEW HOME.
I agree with jno- if the new home belongs to two or more Campbells then it's the Campbells' new home.
But in the context of the question I agree with everyone- no apostrophe