Hi am sorry to hear about your situation, it is not easy but in the end things will hopefully work out for the best and you can be a much happier person.
First of all go visit centrelink and they can steer you in the right direction.
Do you have extended family, close friends who can help you out? I know it maybe hard to ask them but they can sometimes be a real help (I know mine were)
You can get legal advice from Woman's Legal services (not sure of the number) but centrelink should have a brochure.
Lifeline are great if you need someone to talk to - free counselling service.
There is a lot of help out there for single parents you just have to be willing to look for it and ask questions.
I wish you and your kids the best of luck