I have been talking to a colleague of mine, who has a lot of experiences in organising Motorbike trips to the island of Ireland - here is his reply/ suggestions -
"Done many motorcycle tours in Ireland, but nothing re trike. Depending where you are travelling from entering Ireland via Northern Ireland might be an idea, and I suggest you contact Philip McCallen Motorcycles Ltd (https://www.phillipmccallen.com/
), located close to Belfast.
They may or may not have trikes themselves but possibly can point you in the right direction. And they would of course know all about driver licence rules for UK (and Ireland)."
My colleague has also offered to give you some more help/ advise around planning your trip. Could you please send through your e-mail address and I will pass it on to him. He will then get in touch with you directly.
I will delete your e-mail address from your reply, once I have copied it.
I hope this helps for the moment and let us know, if you have any other questions.