There is precedent to the Irish president exercising their power. In 1994 Mary Robinson refused Albert Reynold's request to have the Dáil dissolved (well, let it be known that such a request would be refused), leading to a new government being formed without a general election. If the Queen refused a similar request from a Prime Minister that would be a shock though.

Ah, I was unaware of that, and was thinking more of the 1982 incident where Patrick Hillery shut himself in and avoided answering the phone so as not to be required to dissolve the government.

Both of these fall to me under "refusing to exercise powers" rather than exercising powers though.

Really? I don't understand that. The power isn't in dissolving the Dáil itself, it's in the choice to do if it's deemed appropriate, whether the Taoiseach wants it or not.

When the Queen dissolves parliament she's just going through the motions, it's a formality. If she had refused, say, Theresa May's request for a general election in 2017, saying that there was no need as the Government had a clear majority and Brexit needed to be the focus (and she did this by either hiding down the countryside, not answering her phone or by shooting down the idea preemptively) that would be a huge deal. That would be her exercising her power.

Yikes I can't believe that 1975 event happened and the royal family still remains in their seats.

All of these former British territories are 1 terrorist attack and 1 ambitious politician away from a political crisis.

Roll the dice 10 times, each time one of these monarchs could make a play for power.

Although I'm not even sure how to handle the dissolution of the monarchy without executing everyone. Taking their property only means a foreign state would prop them up.

The British royal family had very little to do with that incident. Yes, the monarch is the de jure head of state, but again in practice she delegates all decisions to the GG.