Yes, it is possible for your cousin to be the daughter of your grandfather's daughter. This is how it would work:
Your mother would be your grandfather's daughter.
If your mother had a sister, she would also be your grandfather's daughter.
Your mother's sister would be your aunt.
And if your aunt had a daughter, she would be your cousin.
Your daughter's grandfather's brother's son is her mother's or father's first cousin and her first cousin, once removed.
Your grandfather's nephew's daughter is your second cousin because you both have a common ancestor in at least one of your grandfather's parents.
cousin
Your grandfather's cousin is your cousin twice removed. Her husband has no direct relationship to you.
3rd cousin
Your 1st cousin's daughter is your 1st cousin once removed.
She will be your aunty
The first cousin of your first cousin is either;also your first cousin, so the daughter is your first cousin once removed, ornot related to you at all, so the daughter is also not related to you.A more complex assessment applies is you are talking abut the second cousins of your first cousin, the first cousin of your second cousin, or another of the many possible cousin relationships.
Your aunt's daughter would be your cousin. If you are related to your aunt by marriage and not blood, then her daughter could be considered your step-cousin.
The nouns in the sentence "Their daughter Mary is your favorite cousin" are "daughter," "Mary" (a proper noun), and "cousin."
Your grandfather's sister is your great aunt.
Your grandfather's great nephew is your second cousin.