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.
If the children are in need of their father’s expenditure then you should not refuse that money, if you do so you commit a sin. If the children are not in need of their father’s expenditure because what you spend on them is sufficient for them then you may reject his offer. However, those who are pubescent and want to take their father’s money should not be prevented from that.
Allah knows best.