You and your second cousin's children are second cousins, once removed.
Your children and your second cousin's children are third cousins.
You and your first cousin's children are first cousins once removed. Your children are their second cousins.
The children of your first cousins are your children's second cousins.The children of your second cousins are your children's third cousins,And so forth.
you and your cousin's children are 2nd cousins. ^^^ This answer is incorrect. your cousin's child would be your first cousin, once removed. (removed meaning a different generation.) Your second cousins share the same great-grandparents, but not the same grandparents. For example, your mother's cousin's child would be your second cousin.
The children of your father and the children of your father's first cousin are second cousins to each other. The children of your father and the children of your father's second cousin are third cousins to each other.
The first cousin of your dad's first cousin is also your your dad's first cousin or is not related to him or to you. The children of two first cousins are second cousins to each other. So the son of the first cousin of your dad's first cousin is either your second cousin, or is not related to you at all.
The children of your mother's first cousins are your second cousins. The children of your mother's second cousins are your third cousins. And so forth.
The children of your mother's first cousins are your second cousins. The children of your mother's second cousins are your third cousins. And so forth.
The children of your parent's first cousins are your second cousins. The children of your parent's second cousins are your third cousins.
Your parent's first cousin's children are your second cousins. Your children and your second cousin's children are third cousins. Your children and your second cousin - or likewise you and the children of your second cousin - are second cousins, once removed. You and your parent's first cousin are first cousins, once removed.
Your first cousin's children are your first cousins, once removed. They are your children's second cousins. Your second cousin's children are your second cousins, once removed. They are your children's third cousins. And so forth.
The children of your mother's first cousins are your second cousins. The children of your mother's second cousins are your third cousins. The children of your mother's third cousins are your fourth cousins. And so forth.
The children of your mother's first cousins are your second cousins. The children of your mother's second cousins are your third cousins.