いわゆる means "so-called" or "what you'd call": the noun after it is a label people already use for this kind of thing. It goes in front of the noun phrase and never changes form.
The noun phrase can start with a clause, as long as it ends in a noun: いわゆるくうきをよむ空気を読むということ, "what's called reading the room". いわゆる does not end a sentence and does not go before a bare verb or adjective.
Like English "so-called", いわゆる can borrow someone else's word without endorsing it. The term often goes in 「」 to make that plain.
いわゆる points to a name that already exists for the thing. いわば ("so to speak") makes up a comparison of your own.
"One big family" is not an established term for a town, so いわゆる does not fit the second sentence.
いわゆる is at home in speech and in writing. Essays and news reports use it when they introduce a technical or fashionable term.