If your daughter-in-law's grandson is a child from a marriage before she married your son, or after their marriage ended, her grandson is not related to you.
If he is a child of the marriage between your son and your daughter-in-law, then he is your great grandson.
The grandson of your nephew is your great great nephew, but few people use that relationship as a form of address. Usually they call relatives by name or business title, not by relationship.
Your grandson and your brother's grandson are second cousins to each other.
Your niece's grandson is are your great-grandnephew.
Your sister would be your grandson's great aunt.
Your first cousin's grandson son is your grandson's third cousin. Your second cousin's grandson is your grandson's fourth cousin. Etc., etc.
Your sister is your grandson's great aunt. He is her great nephew.
Your great aunt's grandson is your second cousin.
You Aunt is you grandson's Great-Great Aunt. Your grandson is your Aunt's Great-Great Nephew.
There is no real blood relationship, as you do not share a common ancestor. You could refer to him as your grandson-in-law. It is probably easier just to call him by name and explain that is your granddaughter's husband.
Your grandson is your brother-in-law's great nephew, and your brother-in-law is your grandson's great uncle.
Nephew?!
Second cousins.