Your cousin.
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.
The grandchildren would be the parents, aunts and uncles, and first cousins once removed, of the great grandchildren.
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.
Second cousins.
You would be Second Cousins
Your child and your nephew are first cousins, so your grandchild and your nephew are first cousins once removed.
second cousins twice removed.
Your grandchild and your niece are first cousins, once removed.
Great nephew. Your children are the first cousins of your niece and your children would be first cousins once removed. Your grandchildren and your niece's child would be second cousins.
Third cousins once removed.
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.
Great grandniece or great grandnephew