Your children are the parents of some of your grandchildren. They are also the aunts or uncles of those of your grandchildren who are not their children.
Even you have a child who is younger than one of your grandchildren, that child is still the aunt or uncle of all those grandchildren.
The grandchildren would be the parents, aunts and uncles, and first cousins once removed, of the great grandchildren.
Your children are the first cousins of your brother's children, and the first cousins once removed of your brother's grandchildren.
You are great great aunt to your niece's grandchild. Your children and your niece's grandchild are first cousins, twice removed.
You are the grandchild of your grandfather. If that grandfather had children other than your parent, and that child had a child - that person is your first cousin and also a grandchild of your grandfather. Your first cousins are, by definition, all those who are not your siblings but are also grandchildren of one of your grandparents. Remember that you have two sets of grandparents. Those first cousins who are related to you through one pair of grandparents are not related to your other grandparents at all.
Your niece is the first cousin of your children and the first cousin, once removed, of your grandchildren.
Your sister's children's children are her grandchildren.Your children and your sister's grand children are first cousins, once removed.Your grandchildren and your sister's grandchildren are second cousins.
Your child and your sister's children are first cousins. Your grandchild and your sister's children are first cousins once removed.
If I knew the answer, I wouldn't have asked it!
In most states the grandchildren would be the legal heirs-at-law. Succession generally goes in descending order if there children and the children of any deceased child would take under the laws of intestacy: parent, child, grandchild, etc. Siblings of the decedent would become the heirs at law only if the decedent had no wife and no children. You can check the laws of intestacy for your state at the related question link below.
Your mother's sister's children are your 1st cousins.
Your first cousin and your grandchildren (your child's children) are first cousins once removed.
Your grandchild through one daughter and your great grandchild through another daughter are second cousins, once removed.