Thank you so much for taking the time to comment.
We did think about running some electrical fencing but we were advised we could face criminal prosecution if a member of the public got a zap, and that's a risk I'm not willing to take. We live in an small outback town so seeking the assistance of a professional isn't really an option for us. I did phone up a dog training centre in NSW to ask some advise. The trainer said it would be a very hard problem to train out of her, if not impossible. For a while I thought she may make a good pig dog given her pray drive, unfortunately after seeking some advise I was told that given she wasn't stock proof they couldn't take the risk with her.
Aside from living in rental accommodation and not being able to build a fully enclosed run, I hate to think of her having to spend the rest of her life on a chain. You see so many dogs around here that spend their whole life on a chain, it's really sad to see.
dancinbcs - After the cat incident I did go to the vets and explain the situation. She told me what I didn't want to hear but I appreciated her honesty; "The dog is a liability and it's only a mater of time before she does something else like this ". It's such a hard decision to make and I couldn't bring myself to do it, but here we are a year down the track facing the same issues. You're right when you say about not getting anything back from her. She isn't an affectionate dog, more like a snooty cat in many respects. She is 4 years old now.
I can't help but feel like I have failed her. I have successfully trained other dogs but she is not like any other dog I have come across. I knew having her pts was always hanging over us but I just wanted to exhaust all other options, hence my post.