Hello Angie
Welcome to Poms in Oz.
Is your ex named on the children's birth certificates? If he is not then I think he would have some difficulty in trying to obstruct you. If he is, then I believe that you will need either his consent or a Court Order. The Court is usually pretty sympathetic towards Mums in your situation, but if your ex won't come to heel quietly, the Court process can be both expensive and slow. I'd suggest consulting a Family Law solicitor in your area.
I also agree with kdal. There have been loads of threads on this very point. Do a search on here and also start a thread in General Dilemmas, I would suggest.
With regard to Hubby, what is an LGV technician, please? Can you find the job on thie list below (on which it may not be called LCV technician.)
A-Z Occupations List - Australian Skills Recognition Information
The ASRI list is not exhaustive, but we might as well keep this simple to start with, I suggest.
Best wishes
Gill