You cannot use the European Small Claim procedure as the UK has now left the EU - which is a shame as it was a very easy to use paper-based system to sue someone in a cross border claim up to 5,000 euro in value.
Your options now are either to start proceedings in the UK and serve them in Ireland on the defendant - or use an Irish law firm (which will cost more and may be uneconomical as a result).
You should send the seller a letter before action to say that you believe your consumer rights have been infringed and that you demand your money back within 14 days, failing which you will issue a small claim.
The attached letter is generic and needs to be tailored (and quote the above breach).
You can sue them and ask the UK court for permission to serve the claim abroad. You need the defendant's address in Ireland for the purposes of the claim form.
You need forms N1 and N510, available here :
The N510 - the first tick box at section 2 is required to be ticked. You then send 3 copies to County County Money Claims Centre, PO Box 527, Salford, M5 0BY for the court to issue.
You must include the issue fee - the fee depends on the sum claimed. The fee is listed on page 5 (under court issued claim) : https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/904862/ex50-eng.pdf
If you pay the fee it needs to be made payable to HMCTS, or your an pay by phone if you ring the court on 0300(###) ###-####/p>
The court will return them to you, you then serve them on the shop by posting them with N215 (available here: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/952023/n215-eng.pdf).
The papers are served on the defendant who then has 14 days to acknowledge the claim - they do this by filling out an acknowledgment of service and they post it to the court. They indicate their intention when they do this, i.e. whether they admit the claim in full or partly, or if they deny the claim.
If they want to defend the claim then their defence is due by 28 days from the date the court served them with the papers. If there is no settlement then the claim will be dealt with at a final hearing which takes anything from 9 to 12 months from when you start the claim - longer if the claim is higher value. You can pursue the claim yourself or use a law firm. For the hearing you can use an advocate if you wish, though it's not compulsory.
Note, if they fail to respond to the court proceedings then you can ask the court for judgment in default - meaning you win in a matter of weeks and you then have a CCJ against the defendant.
I have details of law firms and advocacy agencies if you would like those. Though in a small claim you won't be able to recover their charges from your opponent. A small claims hearing is easy to do, it's quite informal and no lawyer is required.
Once you win then the judgment can be registered at their local civil court in Co Louth for enforcement assuming they still refuse to pay you.
You may find they just pay you after receiving the letter before action – hopefully they will want to avoid litigation.
I hope this helps?