No, she is not related to you. The two of you do not share a common ancestor. Technically the marriage did not make you related, but in most families, they share that relationship.
Are you asking what you call your brothers daughter? Well if you are your brothers daughter is called your niece.
A niece
A niece
Niece
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 sister's daughter is your niece and you are her aunt (if you are a woman) or her uncle (if you are a man).
Your brother's daughter would be your niece.
Your brother's daughter is your niece..and you are her AUNT.
Your brothers ( or sisters ) daughter is your ( niece )
Your niece and your daughter are first cousins to each other.
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.