Your grandchildren and your niece are first cousins, once removed, to each other.
They are first cousins once removed. Your niece's children and your grandchildren will then be 2nd cousins.
your grand niece or nephew in-law (-Kasadie)
(1) Your niece is the daughter of your sibling (2) Your niece and your children are 1st cousins (3) Your grandchildren and your niece's children are 2nd cousins (4) Your g'children and your niece's g'children are 2nd cousins once removed
Your grandchildren and your great niece are second cousins to each other.
Your niece is the first cousin of your children and the first cousin, once removed, of your grandchildren.
Great-great-great Aunt/Uncle. You basically aren't listed as anything else after the first 'great' to that line.
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.
You are your neice's aunt, your neice's children's great aunt, and your neice's grandchildren's great great aunt
great niece
Great grand niece
Your niece's child is your great niece if she is a girl, or your great nephew if he is a boy.
Your niece's grandson is are your great-grandnephew.