Your grandfather's first cousin is your first cousin twice removed. You are both descended from one of your great great great grandparents. His wife, however is not related to you.
Her niece might be the daughter of a sibling of your grandfather's first cousin. (Remember that your aunt can be the wife of your parent's brother or the sister of your parent.) In that case, the niece is your first cousin once removed. The other possibility is that the niece is the daughter of the sibling of the first cousin's wife.
Since the wife is not related to you, her sibling would not be related t you and the wife's niece is not related to you at all.
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