If my sister (who is ill) were to die, would I be granted custody? Should we draw up a will?

In Louisiana, a parent has a paramount right of custody over a non-parent.  In a struggle over custody, a non-parent must show that custody to the parent would cause "substantial harm" to the child.  A relative, such as an aunt, can file for visitation in "extraordinary circumstances," one of which would be the death of the mother.   The best course of action would be for the mother and father to agree upon your having custody in the event of her death,  prior to her death or becoming incapacitated to the extent that she could not make decisions.   If the mother and father are divorced, this may be difficult or impossible to accomplish.   She could appoint you as tutor for the child in her will, but that appointment will not be good against the father unless he agrees, or is found unfit.   He may agree if he is incapable of caring for the child.   Whether or not you or the grandmother would be a more appropriate person to care for the child is a matter of many factors involving the best interest of the child.