I'm going to start dating random women while I still live with my ex
That's probably going to cause some tension. Why do you want to do that?
Dating other girls while living in the same house as her drives her nuts.
It's fine to want to date new people. But it's pretty rude to be dating others while still living with your ex. One of you needs to find a new place to live.
I want to fuck with her mind and see how long it'll take for her to move out.
That's a pretty cruel way to go about getting her to leave. You should just come up with a plan and timeline together about someone moving out. That way you can avoid all the hurt feelings and drama.