As an example of an exceptional circumstance, in a Canada a few years back there was a minority government. The opposition parties banded together and formed a coalition with a plan to take over as a majority.
The Prime minister moved to keep power by requesting the Governor General (Queen's representative) prorogue parliament.
In this circumstance, the Governor General accepted the Prime Minister's request, which ended up rescuing the Conservative minority government. But I think most people agree that if she had decided otherwise, and allowed the majority coalition to take over, that would also have been an acceptable result. So this was, indirectly, the Queen making a ruling on a power struggle between a minority government and a majority opposition.
https://en.m.wikipedia.org/wiki/2008%E2%80%932009_Canadian_p...
The Prime minister moved to keep power by requesting the Governor General (Queen's representative) prorogue parliament.
In this circumstance, the Governor General accepted the Prime Minister's request, which ended up rescuing the Conservative minority government. But I think most people agree that if she had decided otherwise, and allowed the majority coalition to take over, that would also have been an acceptable result. So this was, indirectly, the Queen making a ruling on a power struggle between a minority government and a majority opposition.