You would be Second Cousins
Your grandchild and your niece are first cousins, once removed.
The grandchildren would be the parents, aunts and uncles, and first cousins once removed, of the great grandchildren.
You and your uncle's child are first cousins to each other. You and your uncle's grandchild are first cousins, once removed, to each other.
It would technically be considered your half- cousin since you do have the same grandmother but a different grandfather.
First cousins once removed. They would be your parent's cousin.
Your child and your sister's children are first cousins. Your grandchild and your sister's children are first cousins once removed.
Your child and your sister's child share a common grandparent and are first cousins. Your grandchild and your sister's grandchild share a common great grandparent and are second cousins. There is a generation out of synch, so they would be second cousins once removed.
The grandchild of your grandmother's first cousin is your third cousin. The grandchild of your grandmother's second cousin is your fourth cousin. The grandchild of your grandmother's third cousin is your fifth cousin.
You and your first cousin's grandson are first cousins, twice removed, to each other.
You are great great aunt to your niece's grandchild. Your children and your niece's grandchild are first cousins, twice removed.
First, some of your cousins are not related to your grandmother at all. That is, your father's mother is not related to the cousins you have who are the children of your mother'ssiblings.On the same side of the family, your first cousins are your grandmother's other grandchildren. Your second cousins are your grandmother's great nieces and great nephews. Your third cousins are your grandmother's first cousins, twice removed, your fourth cousins are your grandmothers second cousins, twice removed, etc., etc.
Your father's first cousin's grandchild is your second cousin, once removed. Your father's second cousin's grandchild is your third cousin, once removed. Your father's third cousin's grandchild is your fourth cousin, once removed. And so forth.