They would be second cousins. They share a common Great Grandparent.
3rd cousins
Your daughter and your niece's child are 1st cousins once removed.
Your son and your 1st cousin's child are 2nd cousins.
Your first cousin's child's child (your first cousin's grandchild) is yopur first cousin twice removed.
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 next of kin is your adult child or if your child is a minor, your parents.
Your nephew is your brother's or your sister's son. Your first cousin is also your brother's and your sister's first cousin. Your nephew and your first cousin are therefore first cousins, once removed, to each other. If your first cousin has a child, that child and your nephew are second cousins to each other.
Yes, they are distant cousins.
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.
Your niece and your child are first cousins. Your niece's child and your child are first cousins, once removed. The children of your niece's child and of your child are second cousins to each other.
The mother AND the father are a child's next of kin. Next of kin is determined by legal adoption, marriage and blood. If a child's parents are deceased their next-of-kin would be their siblings by blood or by legal adoption.
Your cousins child is your first cousin once removed.