my great grand-daughter
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.
Grand niece.
Your niece's daughter is your great niece. You are her great aunt or great uncle, depending on your sex.
Great-niece.
Your sister's husband is your children's uncle. They are his nieces and nephews.
pride and prejudice
your 2nd niece...!
You would be a first cousin by marriage, in other words, there is no direct relationship between you.
Your daughter and your niece's child are 1st cousins once removed.
My niece's daughter is my great niece.
There is none. "This is George, my niece's husband." In most families he would referred to as a nephew.
You are her grand uncle (or great aunt) and she is your grand niece.