The grandchildren would be the parents, aunts and uncles, and first cousins once removed, of the great grandchildren.
Your grandmother's sister is your great aunt. (Some would say grand aunt). Your great aunts' grandchild is your second cousin. Her great grandchild is your second cousin, once removed. .
Your brother's grandchild is your great niece (girl) or great nephew (boy). You are their great aunt (if female) or great uncle (if male) Your brother's grandchild'd (great grandchild) is your great grandniece (girl) or great grandnephew (boy). You are their great-great aunt (if female) or great-great uncle (if male)Your grandchild is your brothers grandnephew.
The possessive form for the plural noun great aunts is great aunts'.Example: My three great aunts' house is a great place to visit.
Your sister's great grandchild is your great great niece or great great nephew.
No, first cousin twice removed is NOT the same as third cousin. That is why there are two different terms. Your first cousin twice removed is either the grandchild of your first cousin or the first cousin of one of your grandparents. Which it is depends on which of you is in the generation closest to your common ancestor. Your third cousin is the great grandchild of one of your great great uncles or great great aunts. Another way to describe your third cousin is the great grandchild of one of the siblings of one of your great grandparents.
Grandchild
Your great uncle's grandchild is your second cousin.
There are Aunts, great aunts, great-great aunts, et al. A second aunt would be if you have two aunts and you prefer one over the other. But no there isn't.
Your great-great-great uncle's great-great grandchild is your third cousin, once removed.
Your great grandmother's sister is your great great aunt. Her great grandchild is your third cousin.
Your child and your nephew are first cousins, so your grandchild and your nephew are first cousins once removed.