Your grandfather's second cousin would be your second cousin, twice removed. The twice removed means you are separated by two generations.
Your grandfather's niece is a first cousin of one of your parents. Her son is your second cousin.
cousin
Your grandmother is first cousins with cousin. Your parent would be the second cousin of the cousin's son. That would make you second cousins once removed.
3rd cousin
Your child is your cousin's second cousin. (And he/she is your child's second cousin)
Second cousin
The child of your second cousin is your second cousin, once removed.
Your mother's second cousin is your second cousin once removed.
Your grandfather's great nephew is your second cousin.
Your cousin. You are that person's second cousin.
second cousin
It's your second cousin (: