For an example, I'll quote C.S. Lewis' The Voyage of the Dawn Treader:
One day the cat got into the dairy and twenty of them were at work moving all the milk out; no one thought of moving the cat.
Is there an idiom for this type of situation?
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Depending on the specifics, one could use "taking the scenic route" to the solution.
This wouldn't work for the cat in the dairy, but it does work in problem solving for example.
An overly complicated device could be a Rube Goldberg machine. This could be used for a metaphorical machine as well, or one could use Rube Goldberg process.
Swatting flies with a sledgehammer.
Although maybe that's more of an idiom for using the wrong tool, or for using unnecessary force, rather than for doing something in an unnecessarily complicated way.
EDIT: Actually, Google shows that this idiom has in fact been used with all three meanings.
There's got to be one out there, but I'm mostly drawing a blank.
For what it's worth, according to Wiktionary, the idiom to take/seize a bull by its horns means
Take direct action to solve a problem without looking for other, less demanding, approaches.
but elsewhere I can only find it defined as tackling a difficult situation decisively.
Interestingly, some googling turned up idiomatic expressions in other languages that might fit your bill, particularly Spanish, where
Buscar tres pies al gato
(literally, to look for three feet on a cat) apparently means to unnecessarily complicate something.
In British English Going(all)round the houses is exactly what the OP is looking for. It would seem to be related to the American Robin Hood's(or Robinson's)barn and may be less common among younger people than older ones but is still current. I'm surprised that it hasn't appeared before.