Your daughter and your niece are first cousins. Your daughter and your niece's daughter are first cousins, once removed.
Grand niece.
Great-niece.
your 2nd niece...!
Your daughter and your niece's child are 1st cousins once removed.
My niece's daughter is my great niece.
No he did not. I am one of his grand nieces. He had one daughter.
They are 2nd cousins.
I have three nieces. One of my nieces has had her hair braided. My other two nieces are jealous of her. My niece's braided hair is a honey-golden brown. My nieces' mother is married to my oldest brother.
Your niece's daughter is your grand niece, or, as some would say, your great niece.
your 2nd niece...!
Your niece's daughter is your great niece. You are her great aunt or great uncle, depending on your sex.
Your niece is the daughter of your brother or sister. That relationship is not ended by divorce. If your brother married a woman who already had a daughter (from an earlier marriage), then she would be your "step-niece", and this relationship would, technically, be ended by a later divorce.