how to work well with a person who think so highly of herself, interpersonal skills?

I have to work with a girl who is extremely rude. She thinks that she’s so smart and disrespect my opinions, trying to object them. the problem is I am the director in the group and she told me not to be a tyranny. She always infer or relate negative perspectives from any of my sayings and thinks badly of me.

You do not have to take any back talk , or disrespect or someone constantly undermining your authority, You can go to your boss and give them the particulars, your other employees are probably tired of it too.