Standard sentence structure: «Wir schreiben dem/unserem Großvater einen langen Brief, einen kurzen schreiben wir dem/unserem Onkel.»
In this sentence, «einen langen Brief» is the accusative object (Wen oder was schreiben wir?), while «unserem Großvater» is a dative object. (Wem oder was schreiben wir?)
Both objects can be at the first position respectively:
a) Einen langen Brief schreiben wir dem/unserem Großvater, einen
kurzen dem/unserem Onkel.
b) Unserem Großvater schreiben wir einen langen Brief, unserem Onkel
einen kurzen.
You would put it this way e.g. in a conversation, when you already agreed to write letters, and now you further clarify or suggest that it should be a long letter for one and a short letter for the other.
einen anderen
a bit. The receiver would either think you are a poet or you have a certain reason to place it at first position. The common usage would beWir schreiben unserem Grossvater einen langen Brief, dem Onkel schreiben wir einen anderen
. Because the information is that you address two different persons.