Great grandniece or great grandnephew
Your granddaughter and your sister's granddaughter are second cousins.
Your brother's grandchild would be your great nephew or niece, depending on the gender.
Your child and your sister's child are first cousins. Your grandchild would be a first cousin once removed.
Your sister's daughter is your niece. They are your children's first cousin. Your niece's child would be a grand niece and you would be a great aunt or great uncle.
Great Aunt i think.
Second cousins.
your his great uncle
First cousins once removed.
Grandchild
Your sister's great grandson is your great great nephew. You are his great great uncle, or great great aunt.
your great grandchildren
Great niece or nephew.
Great grand niece
Great aunt or great uncle depending on your gender.
Your child and your nephew are first cousins, so your grandchild and your nephew are first cousins once removed.
The grandchild of your great aunt is your second cousin.
your great cousin twice removed.........i think
You are great great aunt to your niece's grandchild. Your children and your niece's grandchild are first cousins, twice 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.
No, there is nothing wrong with it. People are not likely to be able to figure out that there is any relationship, and if the great great uncle is from the "other side" of your grandchild's family, he is not related to you at all.