At best, I could see a secret Muslim ruling in Connacht.
"Secret" ruling? I would have tought converting people would haven't mix that well with secret.
Anyhow, it's a topic that was relativly studied for presence of Islamic religion outside Islamic states and regions before the modern period. While you could admittedly have a worship from merchants, nothing whatever in written sources or material culture finds support such evidence.
You'd probably need, at minimum, an Al-Andalus that doesn't fracture into taifa states and is able to hold its own against the Franks and so on (which is a challenge in and of itself, the Andalusis seemed to have preferred being wealthy and intellectual to defending their realm)
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1) Franks, while involved in N-E expeditions, didn't really get something from Reconquista. I assume you're talking about Catalans (that had actually more ties with Franks than other spanish peoples)?
If yes, the first part of Reconquista mostly benefited to Castillo-Leonese rulers, while Catalans suffered from both huge divisions and to have a strong taifa (Zaragozza) before them.
2) It would be very hard to prevent a crisis in Al-Andalus resulting in its fracturation. It was a combination of usual hard rule (It asked for strong rulers to prevent having less than a revolt each two years), less productivity of spanish silver mines, localism, and lack of military forces. Which leads to 3.
3) Andalusian didn't preferred being "wealthy and intellectual" to fight (If you ask me that sounds like a weird statement that some could make for our society, "Hey, we grew too nice and civilized while we need to be more agressive".)
First, Almanzor campaigns would proove that, well, wrong.
Second, the problem wasn't that Andalusian society was wealthy and intellectual (something that, past the urban society, isn't that obvious). It was its huge localism : taifa times shows that Arabo-Andalusian didn't minded about fighting if it was about their town or region, showing much little interest pas that.
From there you could probably get a 'rightful heir' going to Spain to shore up support to take the throne? After all, that's how the Normans got their foothold in Ireland.
That Andalusian merchants managed to reach Ireland isn't really an huge feat. It was less interesting than Mediterranean trade, but by and by they showed up.
Think of Abassids coins you could find in Novgorod region, by exemple.
It doesn't mean, however, that Umayyad emirs/caliphs were able to influence on Irish petty-kingdoms or had any kind of formal relationship, and far less to project troops there.
Hell, they focused to do so in Maghrib and Christian Spain, and had to maintain forces or money there continually while not being always sucessful.
The Silver coins were of such high quality the Anglo-Saxon Kings and Viking rulers of Britain and Ireland used to copy them as best they could, including ironically the Shahada, the Islamic script along the outer edges declaring 'There is no God but Allah and Mohammed is his Prophet.'
It's commonly estimated that Andalusian dinar had an influence on westn european coinage, not only in copies of mottos as you said (while it was relativly limited, and that shahada would ironically shows that Anglo-Saxons and Irish weren't really informed about Islamic and Arabic features, to copy that accidently). Offa mancus, by exemple, was a copy of dinar while not copying the shahada, and using false Kufic letters (that were admittedly, used as decoration)
It's of course, showing the extent of Andalusian monetary and commercial influence, far more than showing any political or religious presence.