Detail #249: Nouns and 'Possessive Valency'

Sometimes, nouns can be imagined to have two distinct types of possessors. As examples of this, we could mention quite a few types of emotional states:

my fear of spiders
the police officer's love for donuts

These obviously correlate closely to the arguments of verbs - essentially these are zero-derived verbal nouns, and we find similar things going on for other types of verbal nouns as well. But there are also certain other nouns that can have a similar sort of transitive possession going:

their source of water
their day of rest
their museum of arts

We could of course imagine a language where such transitive possession was much more common, especially if also some kind of ownership for someone elses use was deeply rooted in the culture, giving us things like

her my house (the house she owns, and I use)
her his son (the son she has by him)
their my task (the task they have given me to perform)
your my debt (the debt I have to you)
your my letter (the letter that I sent you)

We can of course imagine ergative-like or nominative-like alignments for such possession, or even inverse or anything, basically. However, one idea that seems quite natural to me would be to have the marking be duplication of the genitive marker.

source of theirs of of water
their water's's source

Maybe only pronouns distinguish the two types of possession morphologically, and word order serves to distinguish the two?

One interesting thing here would also be how interrogative pronouns are dealt with - identical pronouns for both types of possession? Do certain nouns always require dual possession?