Are you asking whether
sin in this sentence could be translated alternatively as "her"?
If so, the answer would be no, it can't.
Si- possessives always refer back to the subject of the sentence, which happens to be
han in this case. Therefore, we'd translate
storebroren sin as "his (own) big brother."
Only if the subject were feminine (e.g.,
jenta, etc.) could we translate
storebroren sin as "her (own) big brother."
Hope this helps! :-)