Your first cousin's daughter is your first cousin, once removed.
Your child and your first cousin's daughter are second cousins to each other.
Your daughter and your first cousin are first cousins, once removed.
Your daughter and your sister's child are first cousins. Your daughter and your sister's grandchild are first cousins, once removed.
Your daughter and your first cousin are first cousins, once removed.
Your daughter and your grandneice are First cousins, once removed.
You are one generation out of synch. That would make you first cousins once removed.
Your daughter and your nephew are first cousins. His daughter is your daughter's first cousin, once removed.
Your daughter and your nephew are first cousins. His daughter is your daughter's first cousin, once removed.
Second cousins once removed.
Your nephew and your daughter are first cousins to each other.Your nephew's son and your daughter are first cousins, once removed, to each other.
Your daughter and your niece are first cousins. Your daughter than your niece's son are first cousin's once removed. Your daughter's child and your niece's child are second cousins to each other.
second-cousin
Your half-brother's daughter is your niece. Your niece and your son are first cousins to each other.