Step parent advice

I need help. Please no bashing. I have been with my guy over 2 years. We are married and have a bean on the way. My step daughter is 6 almost 7. He has full custody of her due to mom's drug use. He is gone for work all the time, leaving me to take care of her constantly. I know it is bad, but it is building resentment between us. The child herself is difficult. We have been to 3 different counselors in the last year to try to help her bullying and lying and hurting our pets. Her school counselor suggested we seek a psychological evaluation and soon before the baby gets here. My husband thinks she is just quirky and little things will work. Everyone around us is saying it isn't normal and she exhibits 9 out of the 10 signs of sociapaths. He thinks I am being dramatic and trying to hard to want perfection. I think he doesn't want to admit something is wrong, which I understand, no parent does. I get in these low points where I feel like he has no right to tell me I'm being dramatic about her when I am always around her. I know her better than anyone in this world. He gets to run away from the problem daily. At this point, I am in self defense mode because she is so mean and hateful and manipulative that I just shut down. I make sure she eats and plays and showers and then tuck her in. We have an appointment on the 16 th. Any words? Kind ones preferably.