they stamped my passport with permission to remain
That’s not a refusal.
A refusal is when they make you sit in the office until the next boat comes, escort you to the boat, and make you go back to the UK.
Merely getting called into the office and being made to sit around for hours while they decide what to do with you, isn’t anything at all (as far as your question). They could do the same thing to their own citizens, who are entitled to enter…
At the end of the day, they plainly admitted you. That’s what matters.
You got the Visa Warning because you were a visa national (needed an Irish Visa) and reached Ireland without a visa, implicitly requesting a waiver claiming to be family member of an EU citizen. You were unable to convince them completely. But for reasons unknown to me, or in compassion, you were allowed a limited entry.
Please note: if you state on your application that you are travelling with your EU family member, then you will be issued with a visa stating “accompanying EU family member”. If you then travel without that EU family member you may be refused entry to Ireland and/or have a visa warning entered on your passport.
Source: Embassy of Ireland in Germany
Although this quote directly relates to visa applications, the fact that there is no border control between ROI and the UK, you were able to report at Irish border without a visa.
You were stopped for extra questioning, your initial story didn’t sound convincing to them, but at the end they were satisfied and let you in. There is absolutely no reason to think of it or report it as a refusal of entry.
So the answer to your question is: No, you were not refused entry.
Credit:stackoverflow.com‘
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