Your sister's daughter is your niece. Your niece's husband is not related to you.
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.
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.
Your niece in law.
Your sister's daughter would be considered your niece.
I cannot see why not. There is no blood relationship between you and your sisters ex-husband.
The relationship to you would be your cousin !
She's pregnant
Brother-in-law
daughter
No. This is a religious relationship, not a family relationship.
Your sister's husband is your children's uncle. They are his nieces and nephews.
First cousins once removed.