Simply put Mrs. Coulter hates her daemon because she hates herself. She causes her daemon pain and experiences pain herself; she berates her daemon because she can't effectively berate herself. She controls her daemon because she wants to control herself.

Is Mrs Coulter severed from her daemon?

Coulter's relationship with her daemon is an utterly normal one, and she is not severed, so this is a change made for the show. While the book series sees Lyra meet severed adults, Mrs Coulter is not one of them.

Why does lyras mothers daemon not speak?

Because a daemon is a reflection of a person's very essence, they share most of the same personality traits. So, when a person tends to be guarded about their emotions and intentions, their daemon may remain silent in order to avoid divulging their inner thoughts and feelings to the world.