Can I give the amount of my vow to my needy son instead of giving it as charity?

There is no objection to giving charity to a son who is indebted or in need. Al-Bukhari reported from Ma'n ibn Yazid al-Sulami that his father intended to give charity, and Ma'n came and took it. His father then disputed the matter with the Prophet, peace and blessings be upon him, who said: "You have what you intended, O Yazid, and you have what you took, O Ma'n." Accordingly, voluntary charity or a vow not specified for a particular person may be given to children who are in need; in fact, they have a greater right to it.