Your cousin's cousin is no relation to you.
You and your first cousin's daughter are first cousin, once removed, to each other. Your child and your first cousin's child are second cousins to each other.
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.
Yes, your "first cousin once removed" is either :your children's "first cousin twice removed" -- if your "first cousin once removed" is the first cousin of your parent, oryour child's "second cousin" if your" first cousin once removed" is the child of your first cousin.
You and your first cousin's daughter are first cousin, once removed, to each other. Your child and your first cousin's child are second cousins to each other.
Your first cousin and your child are first cousins, once removed, to each other. Your second cousins and your child are second cousins, once removed, to each other.
You and the children of your first cousin are first cousins, once removed, to each other. Your children and the children of your first cousin are second cousins to each other.
Your first cousin's child would be your second cousin
If by cousin you mean first cousin, your daughter and your (first) cousin's son's are second cousins to each other.
Your daughter and your second cousin are second cousins once removed to each other.
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.
You and your first cousin's grandson are first cousins, twice removed, to each other.
Yes, the children of your cousins are also your cousins, but a different kind of cousin. The child of your first cousin is your first cousin, once removed. The child of your second cousin is your second cousin, once removed. The child of your first cousin, once removed, is your first cousin, twice removed. On the other hand, your child and the child of your first cousin are second cousins to each other. Your grandchild and the grandchild of your first cousin are third cousins to each other.