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.