My question is about using the adverb "instead of". Am I right in understanding that the said adverb is usually followed by things that did not happen in the past in the story of a speaker?
You picked up someone else's keys. But you should have taken yours. So you could not get to the apartment because someone else's keys didn't fit the lock.
So we cannot say that
You should have taken your keys instead of [..].
It is not correct usage, isn’t it?
There is no reason to assume instead of to have an "irrealis" aspect. It's simply "A, not B". If you take a look at the etymology of instead, you'll see that it simply means "in the place of" or "substituting" (which again has the common latin root situ = place in it).
Your sentence is absolutely fine:
You should have taken your keys instead of someone else's.
Works the other way round, too (but is much more complicated):
You shouldn't have taken someone else's keys instead of yours.
Instead of is a preposition. This preposition combined with a noun is a preposition phrase. This preposition phrase can be an adverb.
Instead of is not a conjunction, which connect 2 similar entities.
