Tips for deal with a Toxic Director

I just became a leader and report directly to a director. I’d like to know if anyone here has been in a similar situation. My director is not a specialist in the area I work in and is always very insecure about the topics, regardless of what I say or present. Since my team is new, she doesn’t trust us yet. On top of that, she doesn’t have the patience to understand the processes. She loves yelling and saying that everything is wrong without even listening to what people have to say. Has anyone ever had to deal with someone like this and managed to turn the situation around? I’ve been working hard to provide very detailed reports with simple explanations so she can understand, but I can’t always make progress on topics during my 1:1 meetings. My team is very afraid of her, and I end up acting as a filter and shield.