I know I was not asked to respond, for I am not Irish, but...

I googled to find out the relative frequency of the terms used in English and German and the result came out to a big surprise for me, for in both cases I would have made the opposite prediction:

'Great Britain and Ireland' is less common than 'British Isles', but 'Großbritannien und Irland' is much more common than 'Britische Inseln'. The last term being used mostly in geography.

As for queens, it is easy in German though not very consistent. We say 'die Königin von...' and insert the country, except when we speak about the English (and some other parts of the world) monarch. Then we say not only colloquially but even in the evening news 'die Queen' (pron.: kveen). Seems natural to us.

Wolfgang