The first two sentences you provide are *possessives*:

> Ask the assistant of yours.

> I hate that friend of yours.

These are also possessives, and they mean the same thing:

> Ask your assistant.

> I hate your friend.


But I think what you're asking about are *double possessives* or *double genitives*.

A double possessive uses both forms of possessive at the same time. For example:

> That book of David's is heavy

There is a rule that states you should not use a double possessive if the object of the prepositional phrase is an *inanimate object*. So it'd be ungrammatical to say:

> The laws of the church's


Instead, you can say:
> The laws of the church

> The church's laws

You might want to avoid double possessives, because a lot of them do sound awkward. There's no one rule that determines whether a double possessive sounds good or not. But nobody would say these:

> I will stay at the place of my friend's.

> I will stay at the place of my friend.

Instead, they would say:

> I will stay at my friend's place.

You *could* say this, because possessive pronouns like "his" work better in double possessives:

> I will stay at that place of his.



There's some more information on this page:

http://www.quickanddirtytips.com/education/grammar/double-possessives