Hello Sam & Lee
Welcome to Poms in Oz.
If you are an Australian Citizen by birth then your children may be Australian Citizens by descent, via you. IN that event, all you would need to do is organise Australian passports for yourself and the children and then obtain a Spouse Visa for your OH. If for any reason the children are not Australian Citizens by descent, then they would be included in OH's Spouse Visa as OH's dependants.
The first thing to to discover, therefore, is whether or not you are an Australian Citizen by birth. Please see this link:
Citizenship by birth
If you were born in Australia prior to 20 August 1986, it looks as if you may indeed be an Australian Citizen by birth. When were you born, please?
If you come within the above provision, you will need to apply for proof of Citizenship:
Proof of Citizenship
You need to complete Form 119 and send everything to the Citizenship section of the Australian High Commission in London:
Visas and migration - Australian High Commission
Sort your own status out first and obtain your Australian passport, I would suggest.
Then you can deal with your children, who I reckon are probably Australian Citizens by descent:
Citizenship by descent
Having sorted yourself out, sort your children out next and obtain Australian passports for them too.
Finally, obtain a Spouse Visa for OH, which is again done via the AHC in London and is processed very quickly:
Family - Visas & Immigration
Partner Migration Booklet
There is actually no other way to do this because Australian Citizens
are not eligible for Australian visas of any description. The UK and Australia both recognise dual Citizenship so there is no problem for you and the children in holding both British and Australian passports.
Having sorted out the Citizenship documents and obtained Aussie passports, plus a Spouse visa for OH, all of you are then free to head for Australia..
Best wishes
Gill