All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Since this father is alive, as you mentioned, then the wealth is his. The wife and the child have no share in his wealth unless he gives it to them and they possess it. Neither the wife, the son nor the daughter own any of it unless he gifts it to them. However, if he gifts his son or one of his daughters something, then the other children can demand justice to be applied (by giving them like he gave the son or daughter).
The predominant opinion of the scholars, is that the father is obliged to be fare when gifting his children. It is not permissible for him to favor one of them over the others without a valid justification, like being in need.
If the father favors one over the rest without an Islamically accepted reason, then he either takes back what he gave to some of his children, or gives the others like he gave them. Ibn Qudaamah said: “If he (the father) gives some of them (the children) a gift or favors some of them, then he is sinful and he is obliged to be fare. This is achieved by either taking back what he gave some of them, or by giving the rest (of the children) the same as he gave those whom he favored.” [End of quote]
Allah knows best.