Grandchild
Your child and your nephew are first cousins, so your grandchild and your nephew are first cousins once removed.
Your niece's child and your grandson's child (your great grandchild) are second cousins, once removed, to each other.
your grandchild
For clarity. let's call your grandmother's aunt "the aunt". Sequence of relationship: (1) The aunt's child and your grandmother are 1st cousins (2) The aunt's grandchild and one of your parents are 2nd cousins (3) The aunt's great grandchild and you are 3rd cousins
A person's grandchild and grand niece are 2nd cousins to each other.
your great grandchildren
Your mother's sister is your aunt. Your aunt's child is your first cousins. Your aunt's grandchild is your first cousin, once removed. Your aunt's great grandchild is your first cousin, twice removed.
Your sister's great grandson is your great great nephew. You are his great great uncle, or great great aunt.
Your grandmother's sister is your great aunt. Her son's child is her grandchild. You and your great aunt's grandchild are second cousins.
Your are a great uncle. I mean, I'm sure you're a wonderful uncle! But great uncle is your relationship. The child is your wife's sister's great grandchild, right? So you are great uncle.
Great niece or nephew.
Great grand niece