Your grandmother's brother is your children's great-granduncle (or great great uncle). They are his great-grandnieces and great-grandnephews.
There is no word in the English language for a relationship between grandmothers of related grandchildren
Your sister's husband is your brother-in-law. Your brother-in-law's brother is not related to you and neither are his children. But he is your sister's brother-in-law and his children are your sister's nieces and nephews.
A brother and a sister, both being children of the same parents, are siblings.
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.
Your brother's children would be your nieces and nephews.
Your brother-in-law's children are your nephews and nieces.
No, your brother's brother-in-law is not related to you unless you and your brother both married children of the same parents and they had another brother. but the the brother-in-law relationship is not through your brother and his marriage, but because he is the brother of your spouse. Technically, the proper introduction would be, "This is my brother's brother-in-law" as there is no direct relationship between the two of you.
If you are referring to YOUR grandmother and grandfather then your children are their great grandchildren. If you are referring to your parents, then your children are their grandchildren. The primary kinship dominates.
your mom's brother would be your uncle
He is his brother-in-law.
your dad's brother would be your uncle
Your daughter is your brother's niece. Your brother is your daughter's uncle