What is the ruling on children depositing 20,000 dollars from their husband's money on top of their father's money, to deceive their brother into thinking that the money has been returned to him, as he is accused of taking the money, and is this considered a valid solution in the sight of Allah?

The basic principle is to think well of a Muslim and not to accuse them without clear proof, as Allah says: (O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin.) [49:12]. Therefore, it is not permissible to accuse your brother or mother of theft. What you did by replacing the money from your husband's funds and not informing your father is not considered a lie or participation in a crime; rather, it is a righteous deed. You should be careful in safeguarding money and not enable your brother to access it to avoid a recurrence of what happened.