You are your neice's aunt, your neice's children's great aunt, and your neice's grandchildren's great great aunt
For clarity, lets call your great great grandfather's niece "the niece". The relationship sequence: (1) The niece is the daughter of your great great grandfather's sibling (2) The niece is a 1st cousin of one of your great grandparents (3) The niece is a 1st cousin once removed of one of your grandparents (4) The niece is a 1st cousin twice removed of one of your parents (5) The niece is your 1st cousin three times removed
You are her great-aunt/uncle. She is your great-niece.
Your niece's child is your great niece if she is a girl, or your great nephew if he is a boy.
My ancestors
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.
Great grand niece
great niece
Your niece's granddaughter is your great great niece. You are her great great aunt (if you are a woman) or her great great uncle (if you are a man).
Your great grandfather's great niece is your 3rd cousin.
Your niece's daughter is your great niece. You are her great aunt or great uncle, depending on your sex.
1st cousin 2x removed
Your niece's grandson is are your great-grandnephew.