Replacing the genitive with a "von" construction

Question

When can a genitive be replaced with a "von" construction?

For instance:

ein Vater der sechs Töchter

ein Vater von sechs Töchtern

And can the English "of" in the context of belonging always be replaced with the German "von"?

Answer 1

People will understand you if you do so, but the result will not always be considered good German. In spoken German it is quite common, while many people are still preferring the genitive in written German and consider it "better" or "more correct". But (no rule without exception) there are also cases where the genitive would make the phrase so difficult to speak that its usage would sound rather strange. E.g. "He is the brother of Klaus" - nobody would say "Er ist Klaus' Bruder". Instead "Er ist der Bruder von Klaus" replaces it completely in spoken and very often in written German. But if the person is named Tom instead of Klaus, people choose between "Er ist Toms Bruder" and "Er ist der Bruder von Tom" as freely as English speakers would choose between "He is Tom's brother" and "He is the brother of Tom".

By using "von", you are actually replacing the genitive with the dative. There is a quite popular book "Der Dativ ist dem Genitiv sein Tod" (which should read "Der Dativ ist der Tod des Genitivs") about this phenomenon and a lot of other mistakes that people (i.e. German native speakers) make in their daily use of the language.

And can the English "of" in the context of belonging always be replaced with the German "von"?

Rather not, and more or less you have a counter example in your question.

"There were 3 girls, and behind them stood a man. He was the father of the young ladies."

should be translated "... Er war der Vater der jungen Damen." The alternative "Er war der Vater von den jungen Damen" is not really wrong, but kind of poor style. (And as other commenters have already pointed out "Er war der Vater von jungen Damen" would mean "He was the father of [some not specifically mentioned] young ladies.)

Update: Browsing the older questions here I found "Deine Fotos" gegen "Fotos von dir". This one adds an important aspect: "von" can have other meanings than belonging or possession, so sometimes you risk to change the meaning of the expression if you replace the genitive with a "von" construction. "Toms Fotos" are the photos that Tom possesses. "Die Fotos von Tom" can have this meaning, too - but without a clear context it would rather be understood as "photos showing Tom".