Your great uncle's niece could be your mother, or your aunt.
It is also possible that she is not related to you at all, as you might not share a common ancestor.
The son of your great niece is your great great nephew. You are his great great uncle.
The great aunt is the great niece's baby's great-great aunt.
Your father's brother is your uncle. You are his niece (if you are female) or his nephew (if you are male).
Your niece's son is your great nephew. You are his great aunt (if you are a woman) or his great uncle (if you are a man).
Your brother's daughter is your niece and his granddaughter is your great niece.
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.
Your grandmother's brother is your great uncle and you are his great niece or great nephew. Your child is his great great niece or great great nephew.
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.
First cousins once removed.
She would be your son's second cousin.
my great grand-daughter