auntie .
Your sister's great grandchild is your great great niece or great great nephew.
The grandchild of your great grandmother's sister is your second cousin, once removed.
The grandchild of your great grandmother's sister is your second cousin once removed.
Your great grandmother's sister is your great great aunt. Her great grandchild is your third cousin.
Your grandmother's sister is your great aunt. Her son's child is her grandchild. You and your great aunt's grandchild are second cousins.
second cousin
Great niece or nephew.
Your great grandfather's sister is your great great aunt. Her grandchild is your parent's second cousin and your second cousin, once removed.
Your sister would be her great aunt and she would be your sisters great niece.
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.
FOR MY OPINON NO BECAUSE GRANDMOTHER IS BLOOD AND ELDERLY AND HALF SISTER IS IN BY MARRIAGE SO YOU DON'T COME IN A FAMILY AND DISREPECT ELDERLY If the half-sister is the mother of the grandchild, or has legal custody of the grandchild through other means, she may have the authority to stop the grandmother fro seeing her grandchild, depending on whether the state in which the grandchild lives has laws establishing grandparents' rights.