I'm curious if they'll be splitting the monarchy between the children or keeping it consistent. Government could actually change quite a bit at this point across much of the west.
I'm not sure what GP is speculating about either but as for succession, AFAIK sovereign countries in the commonwealth have their own rules. The head of state of Canada was not the Queen of England, it was the Queen of Canada, and theoretically nothing would stop the heir to those positions being different. In fact this was momentarily a topic of conversation in Canadian news outlets as the UK was talking about changing the rules of succession to be gender neutral and whether that would make for different heirs if the rest of commonwealth didn't change their rules in step. In practice that was moot since Prince William's firstborn was male.
They are separate, but the different countries have agreed to keep them coordinated. You're right that there was a conversation about the change to absolute primogeniture, with the different realms having to agree to pass the necessary legislation. If one realm had not agreed I suspect the change wouldn't have happened, rather than the succession being split.
That said, there is precedent. Victoria didn't inherit Hanover, which had been in personal union with the UK, because it had different succession laws (which excluded women). So it's just a matter of political will really.
