Your 1st cousin's child is your 1st cousin once removed.
Your 2nd cousin's child is your 2nd cousin once removed.
And so on...
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.
Because that is the way it works. Your cousin's child is your cousin once removed because you are separated by one generation while you and your cousin are of the same generation. Your cousin's child is not your neice or nephew because that relationship is reserved for the children of your brothers and sisters.
Your first cousin's child and your child are second cosins. Your first cousin's grandshild and your child are second cousins, once removed. Your second cousin's child and your child are third cousins. Your second cousin's grandchild and your child are third cousins, once removed.
Your first cousin's child would be your second cousin
Your child and your first cousin's child are second cousins. A full generation is another set of cousins. For example, the second cousins' children will be third cousins, etc. Now here is the tricky part. You are a first cousin once removed to your cousin's child and your cousin is a first cousin once removed from your child.
Your first cousin's child is your child's second cousin. Your second cousin's child is your child's third cousin. Your third cousin's child is your child's fourth cousin. and so forth
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.
Your first cousin's child's child (your first cousin's grandchild) is yopur first cousin twice removed.
You and the child of your first cousin are first cousins once removed.You and your first cousin's child are first 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. It gets more complicated if you are talking about the child of a first or second cousins, etc, once removed or twice removed, etc.
Your cousins child is your first cousin once removed.
The child of your father's first cousin would be your first cousin, once removed. Then when that person has a child, their child will be your first cousin, three times removed. A second cousin is the children of first cousins. For example, your child and your cousin's child are second cousins. Then their children will be second cousins, once removed to each other.