Which construction is preferred in the following?
- Bruder der jungen Frau
- Bruder von junger Frau
Can someone please explain the particular constructions where "von" is preferred genitive over "des/der" and vice versa.
You seem to be confusing the genitive (spelling) case with the more general concept of describing a relationship or ownership.
von requires the dative and would be used like this:
[der] Bruder von der jungen Frau
[der] Bruder von einer jungen Frau
It might be a little confusing that the definite article for female nouns takes the same form for both genitive and dative: der Frau.
Without the von you'd put the "junge Frau" into genitive:
[der] Bruder der jungen Frau
[der] Bruder einer jungen Frau
The option using dative is more colloquial and used in spoken language; the option with genitive is more formal and more appropriate for written language.
I use the Genitive in formal language, also while speaking Standard German. In many German dialects, its usage has been limited or sometimes even non-existant. This idea that it does not exist in spoken language is false, especially when discussing complex topics (like at the university). However, I do not use it while speaking in my dialect.
Perhaps an analogy is best. If you are coming from the English speaking world, it's the same concept as this:
The car of the man is red.
Das Auto/Der Wagen vom Mann ist rot.
Do not let the apostrophe fool you. It was only added to English in non-emphasized syllables. The "s" is a remnant of inflection.
The man's car is red.
Das Auto des Mannes ist rot.