What a load of nonsense!
There is no ownership you silly person. The Royals do not own Australia or get any money from Australia or have any power in Australia that they can reasonably exercise except through its representative and only in specific situations such as war or constitutional disorder.
Australia is an independent and self governing country, member of the UN and has far closer relationships with Singapore, Japan, and USA. Australia is actually a lot more independent as a country than the UK is because the UK is still in the EU and has foreigners imposing laws on the UK whereas only our elected politicians can do this in Australia.
It is a 5 eye partner with the USA, Canada, UK, and New Zealand.
It has its own Foreign Policy and many times it differs from the UK. Australia was never drawn into the Falklands War or the Sinai crisis, but it was drawn into Korea, and Vietnam by the USA. The USA has a lot more power and leverage in Australia than the UK. We are also closer to the USA and always have been.
Our soldiers always got along with their soldiers more than they got along with the Brits because Australians and Americans are very egalitarian and anti establishment. Whilst the average British squaddie was ok, Officers of the British Armed Forces were not like any Australian or American equivalents so we always got on with the Yanks a bit better.
Australia, along with new Zealand, and Canada, share the same Head of State as the UK. But that is our own crown, and the position is ceremonial. It isn't our Government. Out Head of State, Queen Elizabeth of Australia, can't and does not pass laws, interfere in Australian Politics unless asked to suspend parliament.
There is no ownership.
The reason why Prince Charles was schooled in Australia is because the Royal family is very much our own as well and he was indeed sent to a school that is extremely elite and I would say more elite than Eaton.
Not just that, but there is also a connection between the Greek Royals King Constantine and private schools in Australia. yeh who would have thought such a thing but that is the case.
Not many people know this, but King Constantine apparently also holds an official status with the Australian Government and as such travels on one of the RAAFs VIP jets everytime he comes.