Is a gift valid if the children authorize their father to dispose of the gifted property, maintain it, and collect its rent after they learn that a gift must be in the possession of the donee?

If the father is just in the gift among his children, then it is valid and becomes binding upon the donee’s possession and قبض (seizure/taking hold). The possession of real estate is effected by vacating it and enabling the donee to dispose of it as an owner would. Granting a power of attorney to the donor to manage the property’s affairs, such as renting and maintenance, does not affect it. So, if the father has vacated for you what he gifted you, and he was not unjust in his gift, then the gift is binding and valid, and you are entrusted with the matter of renting and maintaining the property.