There are two ways you can have a first cousin, once removed.
The daughter of your first cousin once removed is you first cousin, twice removed. She is also your child's second cousin once removed, and your grandchild's third cousin.
Your daughter is a second cousin once removed to your first cousin twice removed.
Your daughter is related to your first cousins once removed either as a second cousin (same generation) or as a first cousin twice removed.
You and your first cousin share a common grandparent(s). The daughter is out of synch with you by a generation. That means you are first cousins once removed.
You are first cousins once removed.
Your niece and your daughter are first cousins. Your daughter and the daughter of your niece are first Cousins, once removed.
The children of siblings are first cousins, so your daughter and your brother's daughter are first cousins to each other.
They are first cousins.
Your son and your niece are first cousins. Her daughter and your son are first cousins, once removed.
Your daughter and your niece's daughter are first cousins, once removed.
Your niece and your daughter are first cousins to each other.
If your daughter is also your wife's daughter, your daughter and your wife's first cousin are first cousins, once removed, otherwise they are not related.
Your son and your nephew are first cousins to each other. Your son's daughter and your nephew are first cousins once removed.
Your sister's daughter and your son are first cousins to each other. Your sister's daughter and your son's daughter are first cousins, once removed to each other. Your son's daughter and your sister's granddaughter are second cousins to each other.
Your grand-nephew and your daughter are first cousins, once removed.
You and your first cousin's daughter are first cousins, once removed, to each other.
Your niece and your daughter are first cousins. Your niece's daughter and your daughter are first cousins, once removed.