Your daughter and your niece are first cousins
Your daughter and your great grand niece are first cousins, twice removed.
To your sister's daughter you are an aunt (or uncle) and she is your niece. To your niece's daughter ( your sister's granddaughter) you are a great-aunt (or great-uncle) and she is your grand-niece.
Great grand niece
Your niece's daughter is your grand niece, or, as some would say, your great niece.
A person's grandchild and grand niece are 2nd cousins to each other.
You are her grand uncle (or great aunt) and she is your grand niece.
Yes, your niece's daughter is your grand niece. You are her great aunt or great uncle.
The relationship is that of a great great great grand uncle and great great great grand niece
You are great great aunt to your niece's grandchild. Your children and your niece's grandchild are first cousins, twice removed.
my great grand-daughter
Your aunt's daughter is your first cousin, as is your aunt's son.
My niece's daughter is my great niece.
Your niece is the daughter of one of you siblings. Your great grand niece is the great granddaughter of one of your siblings.If your niece and your great grand niece are both descended from the same one of your siblings, then they are grandmother and granddaughter to each other. If they are descended from different siblings, they are first cousins, twice removed, to each other.