It will depend on whether or not you share a common ancestor.
They could also be second cousins, if you all share a Great Grandparent.
If you do not share a common ancestor, there is no relationship between you.
the first cousin and daughter would be second cousins.
Your children and your first cousin's children are second cousins.
Your child and your first cousin's child are second cousins. Your child and your second cousin's child are third cousins to each other.
Your grandson and your first cousin are first cousins, twice removed. Your grandson and your second cousin are second cousins, twice removed. and so forth.
Your children and your first cousin are first cousins, once removed, to each other. Your children and your first cousin's children are second cousins to each other.
They would be second cousins.
Your first cousin's grandchildren are your first cousins, twice removed. Your second cousin's grandchildren are your second cousins, twice removed. And so forth.
Your first cousin's daughter is first cousin once removed to your grandson, and he to her. Your second cousin's daughter is second cousin once removed to your grandson, and he to her.
Your children and your first cousin's children are second cousins.
Your cousin's daughter is your first cousin once removed. Your daughter and your cousin's daughter would be second cousins.
Your first-cousin and your child are first cousins, once removed.
The relationship between your sister's (or brother's) child and your cousin is the same as the relationship between your child and your cousin. Your child and your first cousin are first cousins, once removed. Your child and your second cousin are second cousins, once removed, and so forth.