All of your first cousin's children are your first cousins, once removed. All of your second cousin's children are your second cousins, once removed.
It does not matter if the child is the first , second or tenth child. The English language has only the one term.
Your second cousin's child is your second cousin, once removed.
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 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 would be your second cousin
First cousins once removed. Your child and your nephew are first cousins and there is one generation difference.
Your niece and your son are second cousins. Your niece's child and your son are second cousins once removed.
They would be second cousins. They share a common Great Grandparent.
Your second cousin's siblings are also your second cousins. The children of your second cousins are your second cousins, once removed.
Your child and your second cousin's child are third cousins to each other.
Second cousins
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.
You and the child of your second cousin are second cousins, once removed.