Zakah is only for its recipients while Sadaqa is like the gift

We have collected 2850 dollars for a needy family so that they can purchase car. The family recently migrated from Pakistan and head of household is sick and he cannot work. His son and daughter are working to run the household. Some of the donation was Zakah from some families. Later we found out that family has about 20,000 dollars in their bank account. Should we give the money to the family or divert it to another needy family. The family know that we have the collected money for them and we are holding it back because of the fact that they are suppose to pay Zakah instead of taking Zakah money from community. I need Fatwa on this situation.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. You mentioned that the money you collected is from Zakah and Sadaqa. The Zakah money you had received could not be spent on other than the categories mentioned in this Ayah: {Alms are for the poor and the needy, and those employed to administer the (funds); for those whose hearts have been (recently) reconciled (to the Truth); for those in bondage and in debt; in the cause of Allah; and for the wayfarer: (thus is it) ordained by Allah, ….. }[9:60]. Therefore, you have to spend this money on needy people or needy families. As for the Sadaqa (charity), which is not obligatory, it is like a gift. So, it could be given to other than needy and poor people. Therefore, you may give the amount of Sadaqa (not Zakah) to this family for whom you have collected the money. However, it is better to give it to needy people. Allah knows best.