I am sorry for your previous experience. I hope to make it better.
I must say that European law does not have much to say regarding such a situation, except if you and the bank are located in different countries. From your question, I deduce this is not the case.
However, Irish law offers more than enough possibilities for action, namely in tort law. Tort means a damage suffered by a person due to the non-criminal actions of another person (including a corporation). The damages can be material (such as the costs of your hospital or doctor treatment, if caused by the bank's actions), or moral (for the pain and suffering they have caused).
There is a difference between the kind of action that produced the damages, in terms of easiness of proof. I will illustrate with two scenarios and I am sure you will make the difference. The first one is much more easy to prove than the second. The point of the proof is not only the bank's action, but also the link between what they did and your suffering:
Case 1 - you need to pay for an emergency treatment or, perhaps, a house repair, and the bank, due to its fault, does not forward you the money in time, and therefore something bad happens and you suffer. This would be a clear material fault.
Case 2 - you deal with recalcitrant employees of the bank, and are emotionally charged because they scare you, or threaten and insult you, or threaten to close the account. They also send you scary letters without legal reason. They have a psychological effect on your well-being. This would be a moral damage, but it would be much more work to prove it (usually with witnesses and medical examination reports), and the link between what the bank did and your suffering.
The only relevant law in this respect is the European Convention of Human Rights. However, it is a part of the national legislation of every state in the EU, including Ireland, so the courts automatically take it into account when dealing with cases.
I hope my answer is satisfactory and look forward to your rating.
Dr Ioan-Luca Vlad