great uncle
You would be 2nd cousins, assuming that the brother's wife's granddaughter is also the brother's granddaughter. If the granddaughter is not the granddaughter of the brother, there is no relationship.
Your brother's daughter is your niece and his granddaughter is your great niece.
Your sisters grandson would be your grandnephew.
Your grandfather's brother is your great uncle. Your great uncle's daughter's daughter (his granddaughter) is your second cousin.
No relation ..
Daughter
The relationship between your brother's daughter and your granddaughter is that they are first cousins. This is because your brother's daughter is the child of your sibling, making her a cousin to your child.
Your brother's father-in-law is not related to you unless you and your brother married sisters from the same family. Then he would be your father-in-law, too.
There is no word in the English language for a relationship between grandmothers of related grandchildren
The grandchildren of your grandmother and the grandchildren of any of her siblings (including of her brother) are second cousins to each other.
Your brothers granddaughter is your grandniece.
Your granddaughter is your brother's grand niece (or some would say, great niece).