Your niece and your son or daughter are first cousins. That would make your niece and your grandchild first cousins once removed.
Your niece's child and your grandchild are second cousins.
Your granddaughter and your niece are first cousins, once removed, to each other.
Your granddaughter and your grandniece are second cousins.
Grandchildren of siblings are second cousins to each other.
Your granddaughter and your grandniece are second cousins or third cousins to each other
Your grand daughter and your niece are first cousins once removed to each other.
Second cousins.
your niece
Your granddaughter and grand niece are second cousins to each other.
Great niece
You granddaughter is a great great niece of your aunt. Your aunt is your granddaughter's great great aunt.
Your sister's daughter is your niece. Your sister's granddaughter is your great niece Your sister's granddaughter's daughter (your sister's great granddaughter) is your great great niece. You are her great great aunt, if you are a woman, or her great great uncle, if you are a man.
If you are a woman, you are great great aunt to your niece's granddaughter. If you are a man, you are great great uncle to your niece's granddaughter. In either case, your niece's granddaughter is your great great niece.
Your granddaughter and your grandniece are second cousins or third cousins to each other
Your brothers granddaughter is your grandniece.
Your great great niece is the granddaughter of your niece or nephew. Your daughter and your niece or nephew are first cousins. Your daughter and your great great niece are first cousins, twice removed.
Your children and your husband's niece are first cousins. There is a difference of one generation between them. That makes them first cousins once removed.
Your granddaughter and your niece's son are second cousins.
Your sister's daughter is your niece and her granddaughter is your great niece.