All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
There is nothing wrong with your mother performing Hajj with the money that she received from the employer, if it was given as a donation to help her treat the injury that she suffered as a result of the accident. This is because she owns this money and is entitled to dispose of it as she wishes. However, if the money was paid to her by virtue of a health insurance contract, then we say that the health insurance system in our age is usually of the prohibited kind, and seldom is there an insurance system that complies with the Islamic Sharee'ah, except in a few countries. If the insurance is of the prohibited kind, then it is not permissible to voluntarily subscribe to it. However, if a person is forced to subscribe to it, then it is permissible for him to do so, provided that the money that he receives from it should not be more than what he has paid. He should not benefit from the amount beyond that; rather, he should spend it on the public interests of Muslims and on the poor and needy. If he is one of those poor and needy people, then he may take from this amount according to his needs.
Allaah Knows best.