The relationship is that of a great great great grand uncle and great great great grand niece
Your grand-niece.
Your sisters grandson would be your grandnephew.
Your mothers sisters Granddaughter is your second cousin
Your granddaughter and your sister's grandson are second cousins.
Your son and your sisters child are first cousins. The granddaughter is out of synch by a generation. That will make them first cousins once removed.
WHAT relationship* is your Gramps to your great granddaughter? pretty tricky but (distant sisters one off)
Sisters
Sisters.
Yes
Great neice
Your sister's granddaughter is your great niece and you are her great aunt (if you are a woman) or great uncle (if you are a man).
Brother-in-law