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.
There is no harm, InshaAllah, for your mother to take the money as a compensation for the damage caused to her, because she has a right to take this money, regardless of who paid the compensation, whether it is an insurance company or whoever, as that body was acting on behalf of the person who caused the damage.
This is not considered as helping in sin and enmity. Helping in sin and enmity is when a person signs a contract voluntarily with a commercial insurance bank, not when a person takes compensation on a damage caused to him.
As regards Zakah on this money, it is obligatory after obtaining the said sum of money and when a complete lunar year passes, the scholars from Maliki school of thought mentioned it clearly.
So what you mentioned to your mother to purify the money by paying Zakah on the presumption that it is Haram money is not correct. Because Haram money is not liable for Zakah. Haram money should be spent with the intention of getting rid of it, not with the intention of Sadaqah (alms).
Any way the compensation that was paid to your mother is Halal, (Alhamdulillah)
In such a case, though, one should advise whoever signs a contract with a commercial insurance company, and clarify to him that it is not permissible to deal with such a company if not obliged to do so, and that in case of damage, one should only take the same value as what he has paid.
Allah knows best.