The amount of Sadaqa al-Fitr (in terms of wheat) is 1.75 kg of wheat, no matter where it is paid, if the price equivalent to the amount of wheat is to be paid, the price will be in accordance with the rate at the place where the payer is present. If you celebrate Eid ul Fitr it in Saudi Arabia, then you have to pay the Sadqa Fitr of yourself and your minor children according to the rate in Saudi Arabia irrespective of whether you pay that amount in Saudi Arabia or someone in Pakistan pays with your permission.
As far as your wife and adult children are concerned, if they are in Pakistan, they must pay their sadqa al-Fitr according to where they reside, i.e. Pakistan. However, if you want to pay on their behalf, then It is better to set a price that benefits the poor the most.