Nonetheless you can measure each country's contribution to the Iraq War as a rough proxy for how much they supplicate. The UK contributed by far the most of the three while Canada's involvement was minimal.
For as long as I can remember, the Irish government has been quite deferential towards the US, e.g., allowing the use of Irish airports (mostly Shannon, a civilian airport – but also Casement Aeorodome, the headquarter of the Irish Aer Corps) by US military to carry troops, weapons and – quite possibly (aircraft were never inspected) – victims of “extraordinary rendition”. Every year, our Taoisigh (prime ministers) are always eager to have a photo opportunity with the US president on St. Patrick’s day.
I’m guessing that this is mostly to attract Foreign direct investment into Ireland from US multi-national corporations as can be seen by our notably low rate of corporation tax – and the government’s unwillingness to accept the tax income that the EU considers to be owed to us by Apple. Neo-liberalism has been the dominant political ideology over the past few decades with one former Tánaiste (deputy prime minister) famously declaring that Ireland was (ideologically) closer to Boston than Berlin. This dominance left Ireland particularly vulnerable when the 2008 financial crisis eventually hit us – without the widely touted “soft landing”.
However, the relationship isn’t all bad: a number of US administrations – particularly Bill Clinton’s – helped to bring about the end of armed conflict in Northern Ireland. That was probably the most important political achievement in the recent history of Britain and Ireland (one that Brexiteers, sadly, don’t seem to care about or have forgotten about).
Ireland is officially a neutral country but, as you correctly point out, has a long history of allowing the US to use Shannon as a de facto US Airbase. And, as you also correctly point out, has almost built its entire economy in recent years on providing tax incentives and other bribes for US mega-corporations to set up [nominal] HQ there. The phrases "House of Cards" and "They don't love you back" immediately spring to mind.