If my mother deceased wins a lawsuit, would her lawsuit winnings be divided between my sister and I?

The answer to this depends on the type of lawsuit and your mother's estate.  If your mother had the lawsuit before she passed away, and she did not die from the same injuries that caused the lawsuit, then she had what is known as a "survival claim."  This means that the claim belonged to her.  Now that she is deceased, the claim becomes an asset of her estate.

Did you mother have a will?  If so, the proceeds of a survival claim lawsuit will pass according to the "residuary clause" of her will.  That is the clause that says "all the rest, residue, and remainder of my estate I give to . . . "  Those persons will inherit the proceeds of this survival claim.

If your mother had no will, then the proceeds of the lawsuit will pass according to your state's "statute of descent and distribution."  Usually, a second spouse will inherit some portion of the estate and the deceased person's children will inherit some portion (if they are not the children of the current spouse).  The statutes of descent and distribution usually do not include grandchildren unless the child has also died.  Thus, your children and your sister's children probably will not inherit anything.

If, on the other hand, your mother died from the same injuries that caused the lawsuit, then a "wrongful death" claim exists.  A wrongful death claim is controlled by your state's wrongful death statutes. Those statutes say who can sue and who will recover.  Usually, spouses and children can recover (although in Florida only a spouse can recover) and grandchildren do not (although in Ohio grandchildren can also recover if they were close to their grandparent).  You can see that these statutes are different from state to state.

You will have to consult the injury lawyer to find out what will happen to the lawsuit now that your mother has passed away.  That lawyer should be able to tell you who will receive what.