If she dies and leaves behind a son and a daughter

Praise be to Allah.

If a man or a woman dies and leaves behind male and female children, then the male gets the share of two females, because Allaah says (interpretation of the meaning):

“Allaah commands you as regards your children’s (inheritance): to the male, a portion equal to that of two females”

[al-Nisa’ 4:11]. 

Based on that, if your mother dies and she has no heirs other than you and your sister, i.e., she has no father or mother or grandfather, then her estate is to be divided between you two, and you will have twice what your sister has, so you will have two thirds and she will have one third. If she has any other heir, he will take his share, then the rest is to be divided between you and your sister as described above, i.e., you will have twice what she has. 

But we do not advise you to rush to ask about this now; rather the estate should be looked at and divided according to the situation at the time of death, as no one knows who will inherit from whom or what his situation will be tomorrow except Allaah. 

And Allaah knows best.