Yes, the brother's children would be nieces and nephews of the great-great-grandmother; aka his sister. Great-great grandmother's daughter would be a 1st cousin to the brother's children. She would be the niece of the brother. The great-great grandmother's daughter's daughter would be a 1st cousin once removed in relation to the nieces & nephews. (# of removed depends on generations separating the relatives.) She would be a grand-niece to the brother. The great-great-grandmother's daughter's daughter's son would be a 1st cousin twice removed to the brother's children (nieces and nephews of the gggma) and a great-grand nephew to the brother. The person at this link does an excellent job of explaining this. http://www.ourancestry.com/cousins.html
Your great grandmother's daughter's daughter (i.e. your great grandmother's granddaughter) is you mother, your aunt, or your first cousin once removed.
gammie is the grandmother of all of the children
brother, sister, or cousin
She is your aunt. This is true in most traditions. English does not distinguish between an aunt by marriage (father's brother's wife) or an aunt by blood relation (father's sister).
grandmother/grandma = סבה (savá)the grandmother = סבתא (sávta)Note: the word savta, which means "the grandmother" was borrowed into Modern Hebrew as "grandma" to distinguish it from sava (grandmother). There is no such distinction in Aramaic.
The children of your grandmother's second cousins are your parent's third cousins, and your third cousins, once removed.
* If your husband's children have accepted you as a step-mother and you get along then you would not technically be their true grandmother; but, if his children want you to be part of their children's lives then yes, you could be a grandmother. The children may with to call his former wife 'grandmother; granny, grandma' but they could call you 'nanna; nanna Mary (by your Christian name) or may have a nickname for you.
奶奶 (Nainai) : Grandma, grandmother or 老大娘 (Laoda niang) : Grandma, aunty or 祖母 (Zumu) : Grandmother
Your great grandmother would be your mother's grandmother.
Is your grandson the child of a child you and the person who is the Great grandparent of the step great grand daughter? If so, they would be first cousins once removed, sharing a common ancestor. Otherwise, they are not related.
grandmother
Granny Grandma, Nan , Nana Nama Gram works too.