Your daughter is first cousin once removed to your cousin. Your daughter is second cousin to your cousin's children. Your cousin's children are first cousins once removed to you
Cousins
Your nephew and your daughter are first cousins.
You are First Cousins
You are cousins
Either they are second cousins or technically not related at all. Your cousin's niece would be one of her siblings' children, in which case it would one of your cousin's daughters, or her spouses' niece, in which case there is no blood relationship, but most families would refer to them as a cousin.
Your daughter and your niece are first cousins to each other.
Second cousins
First cousins once removed.
First cousins once removed.
Your children and your niece are first cousins to each other.
First cousins once removed.
Your daughter and your aunt's children are first cousins to each other. Your daughter and your aunt's grandson are first cousins, once removed, to each other.