But as they slept, in the dark quiet of the night, there emerged from inside the horse a group of stealthy Greek warriors.
... in the quiet dark night, a group of sneaking Greek warriors emgerged from inside the horse.

Does the second in the above correctly explain the first? Thanks.
No. "Sneaking" is a pejorative.
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AvangiNo. "Sneaking" is a pejorative.

Thanks, Avangi.

What about the first part, "in the dark quiet of the night?" Why is it stated this way? Does it amount to "in the quiet dark night?" Thanks.
"In the dark quiet night"; "in the quiet dark night" - "quiet" and "dark" are both adjectives. The other version is more dramatic:

"In the dark quiet of the night"; "in the quiet dark of the night" the emboldened words are now nouns. "Night" is now just the object of the preposition "of," and that prepositional phrase also modifies the emboldened words, making them much stronger than "night" was in the simpler versions.