If she is your mother’s neice and you share grandparents she is your first cousin. But it sounds like she is actually your mother’s first cousin because they share grandparents. So she would be your first cousin one time removed.
That said... those relitives I still just call cousins. Or I’d say my mom’s cousin.
I had a relitive that was my grandma’s cousin or my great grandma’s cousin... it was way too confusing. So she would send us birthday cards and say from “Cousin ....”
Random fact... a bit ago I met my 10th cousin one time removed. We were both entering the same college and met at one of those new student things.