It is not permissible to commit fraud in order to take money and assistance from the state in the manner that your mother did, because of what that involves of lying and consuming wealth unlawfully. The burden of sin applies to the one who does that and the one who calls him to do that, but there is no sin on you because you were small at that time, then because you objected to what your mother did. You have to be careful and avoid taking anything of this money. If your father has halaal wealth that is mixed with this money, it is permissible for you to eat from his food in the case of need.
We praise Allah for having enabled you to find work by means of which you can spend on your own maintenance and you do not need your father's maintenance.
You do not have to pay back the government's money, but you do have to advise your parents to stop taking it.
Whatever they took before they knew that it is haraam, they do not have to do anything about, but whatever they took after they learned that it is haraam, if they cannot give it back to the state, they have to get rid of it by giving to the poor and needy.
We ask Allah to increase you in knowledge and guidance.
And Allah knows best.
Reproduced from Islam QA