Is she in college? If so, does she live at home year round or is she just there for the summer between semesters?
My mother and I didn’t get along in high school (for a variety of reasons). Once I went to college (and lived there) our relationship greatly improved. I came back after my first year of college to live with my parents in the summer, and things were even worse. The next two summers I lived in a different state with a friend, and again, our relationship improved. After I graduated from college, I ended up back at my parents for a short time while I was engaged, but I did my own laundry, shopping, cooking and I payed my parents rent ($200 a month). And the relationship was strained, but it remained intact. Now, after being married for 5 years, the relationship is pretty good, but I am quite sure that if I had to live with her again, it would get ugly. We just can’t live together. We each have our own issues and together they are not good. I think that is just how some people (family or not) are.
She is 21, that is certainly old enough to show respect to her mother, even if they don’t get along well. The way she talks about being able to do things herself - well, I think she needs to prove it. If she lives at home, charge her rent. And, she should only be able to live there under some conditions - she has to been in school (and getting good grades), be respectful to her family (not a doormat, but polite and have good manners, no talking back), help with chores around the house, and she has to have at least a part time job (full time one during the summer and a part time during the school year). If she fails to meet any of these agreements, then she has to find a place to live on her own.
Ideally parents shouldn’t have to get to this point, but sometimes our parenting methods are lacking and cause problems, or other circumstances beyond our control and contribute to our children having a disrespectful attitude to us. I think the only way to stop it once it gets to the point you have described with your niece is to show her that her mother is not a doormat and she can’t do everything that she pleases.
It has been my experience (with the people I have know that use to treat their parents similarly) it was because they were spoiled. Mom & dad brought their car, gave them gas money, paid their insurance, payed for college, brought them clothes (and whatever else they wanted), they never had chores, etc etc.
I didn’t have a great relationship with my mom, but I rarely talked back at her, always had chores (without an allowance), I paid for my own car, insurance, gas, and most of my college expenses, and even my wedding.
Right now, it sounds like the daughter is ruling the house, not the mom, and this needs to stop, or it will only hurt her in the long run.