Hi,
Tralee Barracks and Ballymullen Barracks are one and the same. The barracks is still there and is occupied on a part time basis by the Irish Defence Forces. Ballymullen is a short distance outside the town of Tralee in Co. Kerry. The barracks is a little the worst for wear nowadays as it no longer permanently occupied, but most of the original buildings are still intact. If you write to the Officer Commanding they might be able to facilitate a visit, however it is a military post so there is no guarantee that you'd be admitted.
Hope that helps.
Regards,
S.