If you force her to go to a psychologist when she doesn’t want to, it won’t help at all. Worse, she’ll assume that you’ve given up on her and are just palming her off onto the psychologist to “fix” her. Don’t offer her special incentives, either, and don’t threaten her. There is no reason for you to treat her differently in this regard than the way you would treat any of your other students.
She should not be allowed to cause disruptions in class. You need to be really strict on this point for the sake of the other students. The first time per class that she causes a disruption, calmly tell her that her behavior will not be tolerated and continue with your lesson. The next time she does it in the same class, just ignore her. She is clearly crying out for attention, and if she sees that disruptions won’t get her the attention she wants, she’ll stop. But do continue to spend time with her outside of class (inasmuch as she is willing) and try not to lose your patience no matter what she says. You need to show her that you care about her, and that nothing she says or does can change that. Although you may be horrified and cringing inwardly every time she makes fun of Torah or demonstrates how far she has fallen from Yiddishkeit, stay calm and just smile at her. She may be doing some of this for shock value. Don’t allow yourself to be shocked. I know it’s hard and you won’t reach her overnight, but b’ezras Hashem one day she will call you out of the blue and tell you how much you inspired and helped her during her time of difficulty. Much hatzlacha and please keep us posted!