Must the uncle do anything after he gave his daughter Zakat money for her to hand it over to a charity, and the daughter told the organization that it was a sadaqah and not Zakat?

If the charity disbursed your uncle's zakat (definition) for purposes other than its designated channels, based on his daughter's informing them that it was a voluntary charity (sadaqa nafila), then your uncle's obligation for zakat has not yet been discharged, and he must pay it. He may then reclaim the amount from his daughter.

However, if the charity disbursed the amount to the designated recipients of zakat, then your uncle's obligation has been discharged. His daughter's informing them that it was a voluntary charity does not matter, because zakat is a charity (sadaqa), and Allah Almighty and His Messenger have called it charity.

If his daughter's intention was that it be a voluntary charity, the decisive factor is the intention of the father who is paying the zakat. As long as he intended that amount to be zakat and it reached its rightful recipients, then his obligation has been discharged. And if he intended it as zakat after giving the money to his daughter to distribute it as a voluntary charity, that would suffice, provided the recipient was eligible.