I can only imagine this being deeply tied to the concept of Commonwealth, which leads to the hilarious idea of a British Monarch of India.
It could work, in a weird way if you forego an Emperor that dominates them all - fully independent, but with their own common court (which is probably where Representative of the Monarch would go).
So in order to ensure that there are strong ties, but also common laws, trade ties and military alliances (i.e. everything except taxes to Britain)
Brief outline
1) Starting with Canada, Britain has calls for Dominions, and rather than resist, starts naming heirs the Monarchs of the Dominion (no King title, no Kingdom of Canada, just Monarch). However, in order to keep ties, sets up a common court where in the case of a tie, the Monarch of Britain gets the deciding vote. With just the UK and Canada, that obvious leaves Canada a bit overshadowed, but it is a start. That court helps to ensure that disputes are resolved peacefully, and compensation paid between the parties.
2) Australia calls for Dominion status - and now the dynamic changes. Australia and Canada can work together to overrule Britain.
3) India gets a Monarch (or multiple, depends on the strategy/concerns of the time regarding Indian dominance over the Council) - and now there are possibly ties with the UK and Canada on one side, Australia and India on the other, which leads to whoever ties with the UK winning.
But the key is - so that no Monarch can get multiple seats, all Dominions are indivisible, and unmergable with other dominions. Basically if you are the Monarch of Canada, and the heir of the UK, and the UK Monarch dies - you either abdicate Canada, or get skipped over for the UK.
So rather than a US-style federation, we basically have a UK-primacy in a Federation of Dominions, that besides conflict resolution and war, are pretty much independent.
I don't think I can emphasis how important "indivisible, AND unmergable" is - it prevents the rollback of independence, which, if missing, would render the entire exercise pointless.
It could work, in a weird way if you forego an Emperor that dominates them all - fully independent, but with their own common court (which is probably where Representative of the Monarch would go).
So in order to ensure that there are strong ties, but also common laws, trade ties and military alliances (i.e. everything except taxes to Britain)
Brief outline
1) Starting with Canada, Britain has calls for Dominions, and rather than resist, starts naming heirs the Monarchs of the Dominion (no King title, no Kingdom of Canada, just Monarch). However, in order to keep ties, sets up a common court where in the case of a tie, the Monarch of Britain gets the deciding vote. With just the UK and Canada, that obvious leaves Canada a bit overshadowed, but it is a start. That court helps to ensure that disputes are resolved peacefully, and compensation paid between the parties.
2) Australia calls for Dominion status - and now the dynamic changes. Australia and Canada can work together to overrule Britain.
3) India gets a Monarch (or multiple, depends on the strategy/concerns of the time regarding Indian dominance over the Council) - and now there are possibly ties with the UK and Canada on one side, Australia and India on the other, which leads to whoever ties with the UK winning.
But the key is - so that no Monarch can get multiple seats, all Dominions are indivisible, and unmergable with other dominions. Basically if you are the Monarch of Canada, and the heir of the UK, and the UK Monarch dies - you either abdicate Canada, or get skipped over for the UK.
So rather than a US-style federation, we basically have a UK-primacy in a Federation of Dominions, that besides conflict resolution and war, are pretty much independent.
I don't think I can emphasis how important "indivisible, AND unmergable" is - it prevents the rollback of independence, which, if missing, would render the entire exercise pointless.