Your great nephew is your kids' first cousin once removed.
A great great grandchild and a great great nephew of the same person are third cousins, once removed.
Your nephew's son is your great nephew.
Your child and your great nephew's parents would be first cousins. Their children would then be second cousins. And if they have children, they will be third cousins.
Your nephew's daughter's son is your great-great nephew. Your nephew's daughter is your great niece.
First cousin, once removed. Your parent on that side would be a first cousin to the nephew. If the nephew has children, they will be your second cousins. (Of course, your great uncle's nephew could also be your father).
The child of your nephew is your great nephew (if a son) or your great niece (if a daughter).
Your nephew's child is your great nephew (if a boy) or great niece (if a girl). You are his or her great aunt.
Your son and your nephew are First Cousins. The children of your nephew and the children of your son are Second Cousins to each other.
Your borther-in-law's children are your nieces and nephews. You are their uncle or aunt, as is your spouse.
Your grandson and your great nephew are second cousins to each other.
Your great nephew and your granddaughter are second cousins to each other.
great nephew