The Romans occupied England and Wales for centuries. Of course they traded with and visited Ireland. We know they built at least one fort near Dublin. The intriguing question for me is was that just to protect a trading/diplomatic outpost or at one time did they want to occupy Ireland too? Not much hard evidence to answer that.
They were Romans. They wanted to conquer everything they saw.
L
It appears that they found Ireland wasn't particularly troublesome, and was a good trading partner -- actually many trading partners, as there wasn't a single authority, or even the Caig Caigi (five fifths) until the medieval era, and then they kept drinking them up. /rimshot
After the western part of the Roman Empire was sacked and fragmented among barbarian invaders, the British Isles remained on the trade radar (trade-ar?) of the Byzantines, evidenced by Byzantine goods as refuse, discards, grave goods, under burned structures, etc, at Cadbury, other Romano-British sites, including Cornwall.
Time Team S15-E12 From Constantinople to Cornwall, Padstow, North Cornwall