Her 2nd cousin twice removed.
Your 1st cousin's daughter is your 1st cousin once removed.
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."
The daughter of a First Cousin is a First Cousin Once Removed. The daughter of a Second Cousin is a Second Cousin Once Removed The daughter of any kind of cousin Once Removed is the same kind of cousin Twice removed.
Your first cousin's daughter is your first cousin, once removed.
Your daughter's second cousin is your first cousin, once removed, but only if your daughter's second cousin descends from your aunt or uncle. If your daughter's second cousin descends from your spouse's aunt or uncle, then your daughter's second cousin in not related to you.
Your cousin's daughter is your first cousin once removed. Your daughter and your cousin's daughter would be second cousins.
Your mother's first cousin's daughter is your second cousin.
The daughter of your first cousin is your first cousin, once removed.
Your first cousin's daughter is your first cousin once removed. Your second cousin's daughter is your second cousin once removed. It gets more complicated if you are talking about the daughter of a cousin who is one or more times removed.
If your cousin is your 1st cousin then the daughter would be your 2nd cousin. Sorry, WRONG-OOO. YOUR COUSIN'S DAUGHTER IS YOUR FIRST COUSIN, ONCE REMOVED. Your children and your cousin's children would be second cousins.
Your first cousin's daughter is your first cousin, once removed. Your second cousin's daughter is your second cousin, once removed. Your third cousin's daughter is your third cousin, once removed. The daughter of your first cousin, once removed, is either you second cousin or your first cousin twice removed. The daughter of your second cousin, once removed, is either your third cousin or your second cousin twice removed. And it gets more complicated from there.