If you rented out your home in UK and lived with your children in Australia, your place of abode would be "more likely than less likely" to be Australia. Since you would be likely to stay in Australia more than 183 days in a financial year and you couldn't establish either your place of abode is elsewhere or you have no intention to take up residency in Australia, the latter of which is downright hard to prove, I would suggest 870 holders are technically tax residents. Another point is when there's ambiguity, ATO tends to interpret in their favour so they can collect more.
But this is only my opinion, you should certainly ask for professional advice.