Since your niece is your daughter's first cousin, your grand niece (the daughter of your niece) is your daughter's first cousin, once removed.
Your daughter and your niece are first cousins Your daughter and your great grand niece are first cousins, twice removed.
my great grand-daughter
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.
Your wife's niece is also your niece, and her daughter is your great niece. It is to be hoped that you do not have a relationship WITH her, merely TO her.
Your aunt's daughter is your first cousin, as is your aunt's son.
Your daughter-in-law's niece and nephew would be considered your grandchildren's cousins. So, you would be their grandparent-in-law.
Your niece's daughter is your grand niece, or, as some would say, your great niece.
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.
Your niece's son's daughter is your great grand niece. Your niece's son is your grand nephew or your great nephew, whichever term you prefer.
great niece
Your niece's daughter is your grand niece, or, as some would say, your great niece.