Similarly, in a well-known Hanafi jurisprudence book it is stated:
“ويجوز أن يؤديها غيره بإذنه.”
This means that Sadaqat al-Fitr may be paid by another person with one’s permission.(Al-Fatawa al-Hindiyyah, 1/191)
If your father has paid the Fitrana on behalf of you, your wife, and your children, it is generally considered valid, provided that it was given to a deserving poor person and the amount was correct. In Islamic law, the basic responsibility is on the head of the family to pay Sadaqat al-Fitr on behalf of those who are under his financial care. Since you are responsible for your wife and children, the primary obligation was on you, but if your father paid it with your permission or general consent, then it is considered fulfilled and there is no need to pay it again.
Paying Fitrana according to the Pakistani calculation is also acceptable if your family lives in Pakistan and the charity was given there, because many scholars allow Sadaqat al-Fitr to be calculated according to the place where it is distributed to the needy.
Therefore, if your father has paid the correct amount of Fitrana for you, your wife, and your children and gave it to a deserving person, it is considered sufficient and your obligation has been fulfilled. If you had prior knowledge or general approval of this, then there is no problem with it.