You sound where I was not all that long ago, my ex and I did the whole flat mate thing for about 8 months. It wasn't ideal, I didn't know how to go. I didn't want the kids thinking it was normal either for a home to run like that.
Finally I took the leap and left, it was hard I won't lie but its a year since I moved out and I'm so much better for it.
I moved back closer to my parents, the kids adjusted to new area, school etc.
Centrelink couldn't help me til I'd signed a lease, that was biggest problem luckily for me we agreed for me to take money out of the mortgage we had to pay first month rent and bond for my new place then once that was in place I could set up centrelink. You can apply for seperated under one roof but the form is quite long.
As for belongings, take the big stuff, washing machine, dryer, fridge, then all your stuff and kids stuff, we devided plates etc but really you can buy $12 dinner sets at kmart, I wouldn't worry too much bout small stuff.
Will your ex help you through the move?
As for the guilt, well I still do feel guilty at times. I get my eldest saying she wants us all to live together but I do know its better now having everyone getting along than living in a home of tension and unhappiness.
Feel free to ask me any other questions.