The first doesn’t look correct to me. I’d also have said the latter, where did you see it ?

However, a common phrase is “Ça nous changera les idées” (“(se) changer les idées” is the generic form). Maybe it was a deformation, a mix of several expressions, if said orally it wouldn’t be that surprising.

The last thing I’m thinking of is maybe the sentence was “Ça nous détournera les idées du déménagement” as in “we will think about something else than the moving“, it talks about the moving specifically, while the other are talking about a hypothetical moving, or a moving to come.

EDIT : I see you changed your question, do you still feel the first one is weird ? In english I think it would be “that would take our minds off the moving“, and the second one is not correct. It would be with “de“, talking about, as I said, a hypothetical moving, or one to come, but with “du” it’s not !

How to use the verb “détourner” ?

Well, french language mostly use “détourner” when you a hi-jack an airplane, or when you use an object to not fill his primal function, like when you do music with your gameboy you can say that “j’ai détourné l’objet de sa fonction”

In your case, we use more usually “se changer les idées/s’aérer l’esprit”, idiomatics expressions.