I need help with problems at my new job.

2 months ago I took a Director position in a hospital, leaving a job of 10 years. This is my first real leadership role. I found out that 7 people had quit from my new position and the hospital had a temporary employee until I was hired. Things have been okay until the fill in, who was overseeing me, left. Since then, I have been disrespected and treated poorly by my employees. The staff does not seem to see me as a boss. My assistant threw away my business cards, calendar and argues about her duties. It was suggested that I fire her but I wanted to have a discussion with her prior to this step. The discussion did not go well and she expressed she did not plan on changing her behaviors. Fast forward to today, I had to give her a final warning that she would be terminated with any further behavior issues. She has developed a clique of women who whisper about me. She has initiated a harassment claim against me. The work environment is so disheartening .People treat me terrible. I have discussed this with my boss but I don’t see how I am going to make it through with all these problems. I feel like there is something wrong with me the way the workplace has rejected me. Please advise.