father's surname is not approved

Please,we really need an advice. My step sisters and brothers are now using their live birth for their school records, last year, we requested for their nso, the problem was in their NSO it's still our mother's surname which was used by them. The situation is like this, when they were born, the first wife of their father was still alive, that means our mother is his mistress. That time they used the surname of our mother, but a year after the death of the first wife of their father (which is my stepfather)they transferred the surname of my stepsisters to the surname of their father, legal procedures had been followed and done, (I don't know what were those, what I'm sure about is that, their live birth were already okay, there was already a stamp and other authentication documents to prove of their legitimization as the daughters and sons of their father)The big problem now is,WHY is that their surname in their NSO was not change yet? Who causes the fault? When we applied for an endorsement for legitimization or i don't know what was filed, it was disapproved by the NSO. Their reason was these children were born when the first wife was still alive. Could they not use their father's surname because of those reasons? Our mother and my stepfather got married last 1997, their first daughter was born 1992, then 1994, then 1996, after their marriage, they had processed documents. I don't know what happen now. What was lacking? It was recommended to have acknowledgement from the father, another problem is, their father (my stepfather is already dead now. WHAT SHALL WE DO?We do need the NSO now where they use the surnameof their father as what they used in their school records...please gihve mee an advice..

Thank you