Yes, you're her grandparent's sibling.
Your daughter and your niece's daughter are first cousins, once removed.
Your niece and your daughter are first cousins. Your daughter and the daughter of your niece are first Cousins, once removed.
Your niece's husband's daughter is also your niece's daughter and therefore she is your great niece. You are her great aunt or great uncle, depending on your sex. If your niece's husband's daughter is from a previous marriage, and so not also your niece's daughter, you are not related to her. Of course, if your niece adopts her, then she is your adopted great niece. If your niece married her husband while his daughter was very young and everyone has been treating her as your niece's daughter, then you can call her your great niece if you want, but that does not change the fact that you have no common ancestors and therefore are not related to each other.
Your niece and your daughter are first cousins to each other.
Your sister's daughter is your niece. Your niece's husband is not related to you.
They are first cousins.
Your mother's niece is your first cousin. Your first cousin's daughter is your first cousin, once removed.
Your son and your niece are first cousins. Her daughter and your son are first cousins, once removed.
your grand niece or nephew in-law (-Kasadie)
They are second cousins
Your brother's daughter is your niece. You are her aunt (if you are a woman) or her uncle (if you are a man).
Your brother's sister is your daughter's aunt, and your daughter is your brother's, and his sister's, niece.