[Mesorah] Possesive phrases

[Kenneth Miller via Mesorah]

I am currently thinking about the meaning and translation of phrases which have a possessive attached to them. Two examples, both from Retzeh of Birkas Hamazon:

Yom Menuchaseinu
Eer Kodshecha

How do we understand these? One way is to take the phrase as a unit, and apply the possessive to the phrase:

our rest-day
Your holy-city

But one could also take the second word as a unit, which details the first word:

day of our-rest
city of Your-holiness

My question is whether there are grammatical rules for this, or must it depend on context. I cam easily imagine a grammatical rule which says that this hinges on whether the second word is a noun or a adjective.  The problem is that Menucha is clearly a noun, but in this case, do we see it as a modifier ("our rest-day") or as independent ("day of our-rest")?

(A related problem in my mind is that although Kedusha is clearly a noun, I'm much less confident about Kodesh. I want to call it an adjective, but I have vague memories of it also being a noun.)

Similar questions can be asked about longer phrases, such as "Moshiach ben David avdecha". Does this mean "Your servant Moshiach-ben-David" or "Moshiach, the son of Your-servant-David"?

If the response is that these sort of phrases are inherently vague and ambiguous, that is an entirely acceptable answer, freeing translators to interpret such phrases to their liking. But if there is some sort of objective rule, then I'd like to hear more about it. Any thoughts greatly appreciated. 

Akiva Miller
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