'zu' for 'to'?
It's not needed in German in this sense. The 'to' is implied by the Datif/Dative tense of the object of the sentence (which is 'the father'): so it is '...eurEM Vater' (not '...euren Vater' as in would be in a normal objective/Akkusatif/Accusative tense).
So '...eurem Vater' means '...to our father'. Make sense?
The German sentence is not understood . 'Ihr schreibt' is the plural form, indicating that more persons are writing in parallel. 'Eurem Vater' indicates that these many persons are writing in parallel to one single person that is the father of all of them ?? I would expect: 'ihr schreibt euren Vätern'