She could be
a) your mother
b) another aunt by marriage, or by blood (i.e. your mother's sister).
(Note that under -b- your father's sister's sister-in-law could also be his sister-in-law too.)
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Your father's sister is your aunt.
Her sister-in-law may be her husband's sister. You are not related to that person.
But her sister-in-law could also be the wife of one of her brothers. That would include your mother, as well as the wife of any other brother your father might have. Your father's brothers are your uncles and their wives are also your aunts.
Your daughter and your nephew are first cousins. His daughter is your daughter's first cousin, once removed.
Second cousins once removed.
second-cousin
Nephews and nieces
3rd cousin
2nd uncle I believe
You are their great aunt/uncle.
Your borther-in-law's children are your nieces and nephews. You are their uncle or aunt, as is your spouse.
Your uncle-by-marriage's nephews might be you and your siblings. You are your uncle's nephew or niece.They might be the children of your aunt's siblings (your aunt being his wife), in which case they are your cousins.If they are your uncle's nephews by virtue of being children of his siblings, they are no relation to you at all.
He would be his great great great uncle
You would be his Great Uncle and he would be your Great Nephew.
They would be great nieces or great nephews.