Dealing with a selfish ex of partner, is it worth the stress?
Welcome here to the forum. It's a good idea to come as you can get to see if you search the threads how others have managed (or not) similar situations.
Unfortunately the divorce is never the end of the relationship if there are kids, and if she is greedy, irrational and dishonest then trying to deal with her is, as you have found, a nightmare. In fact impossible. It is also quite common.
You realy do need outside advice on your options, and I would suggest you go to a post separation counseling service such as is done by Relationships Australia - 1300 364 277 - who do charge.
I'm sure there are many others, perhaps if you rang our 24/7 Help line - 1300 22 4636 - they may have some ideas about help in your area.
There would appear to be a fair number of things she does that might constitute lack of child care if she abandons an eight year old. This is one of the things the counseling service may be able to clarify.
Similarly her Centrelink payments may be inappropriate.
I get the feeling -my apologies if I'm wrong - that you are the strong one in the relationship and your partner is not one to fight. This is unfair, it puts the weight on your shoulders. Do you think if there was some way to get the ex dealt with then you would wish to remain together?
You be had good advice from Croix.
The future might surprise you as it did me. At 12yo my eldest came to live with me. That cancelled out the child support. She left her mother's care simply because her mother treated her the same as she treated me- with narcissism. Let's call it karma.
Start making a log of all times and dates she untimely drips the kids off. If you both have the children beyond a certain amount you can have child support reduced. Check the CSA website.
10 years will go quickly. When my youngest reached 18yo I informed their mother never to contact me- ever!. I had been treated appallingly over many years.
So, I'm glad you vented and hope you feel better. As a team I would solidify your relationship with your partner because as a team you are stronger.
Finally, dedicate yourselves to the welfare of the children . You won't change her mentality so any thoughts about her is wasted time. Remove her from messing with your life mentally as best you can.