In order to answer a question, it needs to make sense! That would help...
Since this is your mom's partner's niece, she is a part of your family. The best thing would be for you to view her as family so there is no problem in the family. If you all like each other like family and find other people to be intimate with, your mom and partner would have a easier time with all of you.
Your mother's niece is your first cousin. Your first cousin's daughter is your first cousin, once removed.
Father- son-brother- niece- cousin-another family member
Your cousin is your Uncle/Aunt's son/daughter. Your niece is your brother/sister's daughter. So your parent's niece is your cousin.
Since your niece is your daughter's first cousin, your grand niece (the daughter of your niece) is your daughter's first cousin, once removed.
A niece. How could you not know that
cousin daughter
Your father's niece is your first cousin, and her daughter is your first cousin, once removed.
Your first cousin's niece is the daughter of her brother or sister. Your first cousin's brothers and sisters are also your first cousins. So your first cousin's niece is the daughter of your first cousin and is therefore your first cousin, once removed.
There may be no relationship. If you do not share a common ancestor, you are not technically related.
cousin, niece, nephew, aunt, uncle, grandparent
Your niece is the first cousin of your children and the first cousin, once removed, of your grandchildren.