I've been wanting to draw this for like, a year xDDD But never got round to it.
This is my NUMBER ONE favourite fan theory!
Here's my take on it:
During Scar's reign, Nala gives birth to Vitani (Probably with Scar, like the deleted scene where he tries to seduce her), and knowing that Scar would kill her (She would not be important in his 'host of little Scars') she takes her to Zira (I always liked the idea they were friends at this point), knowing that Scar is in good terms with her, and would spare the cub, and begs her to hide Vitani until she (Zira) gives birth to the cub she is expecting (Kovu), then claim that Vitani is Kovu's twin! After Zira reluctantly accepts, Nala heads back to claim to Scar that the cub did not make the birth.
After the battle between Simba and Scar, as Nala chooses to stay in the Pridelands instead of go with Zira, Zira grows a hatred towards Nala and feels betrayed.
As an adolescent, Vitani learns of her real past and grows a bitter anger towards Nala (after being fed lies by Zira that Scar would have spared her and Nala just didn't want her as she was weak at birth), knowing that she could have lived a healthy life in the Pridelands, rather than rot away in the Outlands-hence her bitterness towards Nala in the final battle scene, and the the hint of a deeper meaning in the above quote~