Melby, print off and keep that email. It screams of him trying to make himself look good and taking no responsibility of his own. It may prove useful.
Why don't you keep up the emailing, unless you find it draining. Its just not appropriate to bring up issues in front of the kids, which is what he does because he knows you are the better person and WILL back off because they are there.
You might even be able to sort things, or get somewhere via email because at least you can step back and consider what he says, or go kick a wall when you don't, compose yourself and reply in your own time.
Send him an email saying again, you will only communicate issues with a mediator or via email. Just a suggestion if you think if might work.

Lovin - get on the Centrelink website, its pretty easy to navigate and you can run the payment calculator to see what you may be eligible to receive. Its a good place to start.