I would leave, as soon as possible.
You're unhappy, one of your kids is unhappy, the other one was presumably happy in the UK so will be Ok in either place.
Your DH has told you to take the kids and go back if you want to, which suggests to me your relationship isn’t as strong as you thought.
You don’t say how old the kids are, but the longer you stay, the more they'll see Australia as home. I have friends who took their primary age kids to America, intending to stay for about 5 years for work. 5 years later and their kids are teens now, they’re basically American, and the Uk means nothing to them. So the parents are stuck there. My Mum had a friend who went to Australia with young kids, came back some years later, but one by one as the kids turned 18 they went back to Australia, because to them it was home.
You had a deal with your husband to try it for a year, and he’s gone back on that deal.
I often read threads on here about how awful the UK is, and how lots of people want to emigrate. People seem to imagine that all their problems will disappear in another country, but often what happens is the problems are still there, but the support network is gone.