The second axe is a bit bizarre, it was found stuck in a wall at the iron age fort at Dun Aonghusa, some think it was a prank or just very fortuitous! It's presence there is pretty suspect and not thought to add any weight to paleolithic habitation. I think this is the one on display in the museum.
Personally I have no problem with paleolithic activity in Ireland. I have more of a problem with there being none to be honest. Ireland was much more heavily glaciated than most of England with only a bit of Wexford escaping. It is said that the Mourne Mountains were once as high as Everest. If they can be worn down to comparative pimples then there's no hope of any traces of human activity surviving from before the ice ages.
There's a cave in Derry (I think) that has some very interesting scratches on the walls. There's a lot of more modern stuff in there, too, but some of them seem a lot older. (Note to self: climb up to the bugger one day and take a peak!)
