How do you differentiate between the cases? The direct objects are obvious, however switching between them mid-sentence is quite confusing. How do you know when to use the genitive different from the dative or the nominative? What are the indicators that a specific case is needed and how do you know when the case is being used by others?
The genitive is used to denote possesion. "Der Vater des Kindes" translates to "The father of the child".
Dative can be triggered by certain verbs which you'll probably just have to memorize. Additionally, it denotes when something is done "for" or "to" someone. "Ich schicke ihm den Brief". "ihm" being the dative case (sending the letter "to him").
Also "den Brief" takes the accusative because it is receiving the action, i.e. it is the object being "sent", although I think you said you understand that part.
Hope this helps!