I begin with the following translations of the sentence "This is my father":
Þetta er faðir minn.
Dette er faren min.
Det her er min far.
Det här är min far.
All languages above descend from Old Norse, which is almost the same as modern Icelandic. No major grammar changes happened in either West Scandinavian languages (Faroese and Icelandic) regarding pronoun usage, so we may quite happily consider all other North Germanic languages to be the offspring of Icelandic.
Now, I know almost nothing about Faroese, but I'm pretty sure the pronoun structure is the same as in Icelandic: the possessive pronoun comes after the possession. Since they're both West Scandinavian, one might think this was a characteristic of this particular set of languages, but Bokmål has this feature too. I'm not sure if Bokmål is a West or East Scandinavian language (like Swedish and Danish), but I'd assume it to belong to the East branch, since it is so close to Swedish and has virtually no cases.
That being said, I'd really like to see an explanation for the fact that even though all those languages come from the same ancestor and are so geographically and historically correlated, the pronoun structure in the East branch has evolved to accommodate the possessives before the possession. If Bokmål is really an East Scandinavian language, why didn't this happen to it¹? What mechanism could explain these possessive pronoun usages in languages that evolved from the same ancestor?
¹: This is really a secondary question, because I might be wrong assuming it belongs to the East branch.