Definitely stop paying bills. Give her a weeks notice and cancel everything that is in your name connected to that house!

Get another solicitor if you are not happy with the one you currently have.

Talk to Relationships Australia. Try mediation again. Make notes about her cancelling etc. It will all go in your favour when it gets to court. Take notes about everything little thing. If she promises something and doesn't deliver, make a note etc.

Lastly, do not play her game. It sounds like she is incredibly hurt by the breakdown of your marriage and she is lashing out. Try to be sympathetic but do not be a punching bag or doormat!