All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
In principle, your friend did not backbite you, and accusing her without evidence is not permissible especially that she denied having done so. You do not have any evidence to prove that she backbited you, and you have no reason for hating her after she denied what is attributed to her.
Therefore, you should treat her as if nothing had happened especially that she is one of your relatives.
Even if we presume that what is attributed to her is correct, you are religiously urged to forgive and forget, and there is much excellence in forgiving as we clarified in Fatwa 84351.
In any case, her family is innocent from this matter and you should not hate them or wish that bad things would happen to them without any sound reason.
Finally, it should be mentioned that if you fear to be harmed by her, then you may be cautious while dealing with her.
Allaah Knows best.