This. ^ Go home @mummaAusUk You sound so sad and blue, and your posts are making me feel teary. I can't imagine what it would be like to be isolated 10,000 miles from home, on the other side of the world, with no family (other than my DC who are also unhappy,) no support, no-one to talk to, no friends, and no work either so not even any work colleagues. Have any neighbours tried to connect with you/speak to you? Have you spoke to them?
It would have upset me so much being stuck in Australia with my young DC, with my parents, and siblings, and cousins, and aunts, and uncles, and grandparents, and friends, and nieces and nephews, and neighbours, (and my whole life and my whole past,) back in the UK.
This has never happened to me, but I feel your pain ... I think you need to come home. JMO. As some posters have said, what rights will you even have if your partner leaves you for another woman? You have no job, you're not married to him, you will very likely be stranded and in penury, and he may be able to stop you taking the children back to the UK.
Leave NOW while he is saying you can go with them. It is not a given, that your children will have a better life in Australia than in the UK, (as a pp said.) You sound very close to your family back in the UK, and I think you are going to struggle to settle in Australia. In fact, you may never do.
It would have killed me especially - to have moved away from my parents, siblings, nieces and nephews, and grandparents. My family are working class, and not rich, and they could never have afforded to travel to see us. As I said, it's impossible to keep the connection, and still be a big part of your family's life when you're on the other side of the planet. (In fact it's hard to be a part of it at all...) No matter what people say, things are never the same again, when you move abroad multiple 1000s of miles away (to live.)