daughter
Let's see if we can unravel this. Your sister's husband's father's brother is your sister's husband's uncle. The uncle's daughter is your sister's husband's cousin. There is no relationship to your sister, unless your sister wants to call her a cousin-in-law. To break it down to its simplest terms: She is your brother-in-law's cousin and no relationship to you.
You daughter's husband's mother is your daughter's mother-in-law. The English language has no term for a relationship between you and your daughter's mother-in-law.
Your sister's daughter is your niece. Your niece's husband is not related to you.
Your mothers husband would be your step father and you would be a step son or step daughter.
Your daughter's husband is your son-in-law.
She's pregnant
If he has adopted her then he is her father and has all of the biological fathers rights transferred to him at adoption. If adopted yes
The English language recognizes no relationship between you and your husband's great uncle.
Your husband's sister is your sister in-law.
Your wife's brother's daughter is her niece and your wife is her niece's aunt. Although you have no genetic relationship to your wife's niece, by convention your wife's niece is considered to be your niece and you are her uncle.
Your sister-in-law's husband may be your brother. If so then the brother-in-law is either your husband, in which case the daughter is your daughter; or the brother-in-law is your brother, so the daughter is your niece or the brother-in-law is the brother of another sibling's spouse, in which case the daughter is still your niece If your sister-in-law's husband is not your brother, then he is not related to you and his brother-in-law's daughter is not related to you.
She would be your niece. You're her aunt by marriage !