A:
The money earned from working in a restaurant that serves alcohol and other unlawful things is unlawful. Receiving such money does not oblige your mother to perform Hajj or makes her legally competent to perform it. The legally considerable competence is having lawful money that enables her to travel from and return to her country along with her Mahram (spouse or permanently unmarriageable relative). Allah is Good and He therefore, accepts only that which is good. Allah (Exalted be He) states:
O you who believe! Spend of the good things which you have (legally) earned, and of that which We have produced from the earth for you, and do not aim at that which is bad to spend from it, (though) you would not accept it save if you close your eyes and tolerate therein.
Moreover, one is not permitted to buy food, (Part No. 14; Page No. 418) clothes or a car using unlawful money. One should get rid of that money by spending it for public benefit or paying it as a charity. Your mother should not accept such unlawful money in the future. Moreover, you should advise your brother not to work in such restaurants and that he has to repent to Allah from this sin. Whosoever fears Allah and keeps his duty to Him, He will make a way for him to get out from every difficulty and will provide for him from where he does not expect. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.