The thing she wants most is to be number one for her mother or at least receive the same amount of love as Anu. And this will be the area in which Nivi will always fail. That space is reserved solely for Anu. How must it feel to grow up knowing that?
Some sisters may decide not to try at all and worship their brother the way the mom does. But not out Nivi. Her love and protectiveness of Anu is always evident but in addition to that two things stand out. (i) she has become competitive of Anu and is always trying to prove herself as good or even better than him; and (ii) she tries to emulate her mother and her mother snobbery hoping I presume that this will make her mom love her more. Not only does it not succeed but she is actually emulating the worst bits of her mother.
This is probably also why she does not allow herself to love Anupam. He was her fun on the side, the guy she flirted with but probably would never have brought home because he did not meet her mom's standards. She can therefore never forgive him for tricking her into marriage - or at least that's what she thinks.
Nivedita is such an interesting character. She can so easily appear a villain and I suspect will be given some bad things to do by the writers...and yet I don't think she is a villain. She is probably the greyest of the characters and I am extremely keen for the writer to delve into the murky water.