Grandparents have the right of knowing what is happening in their children's family, but they shouldn't abuse this. They also have the right of offering advice when they are asked or when the situation become critical.
Grandparents have no rights that there children do not grant them. In the case of the death of their child, grandparents in most states can petition for visitation with grandchildren.
Each state has different laws regarding this. Generally if the grandparent can prove that their interaction with the children is positive for the children the court will allow it.
Grandparents rights should be allowing regular visits, participating in their grandchildrens lives, and have the right to take custody, if grandparent is more mentally and financially stable than the parent.