Your case is very complicated, and I am sad that it took so long for you to find his new address and property. The main problem here is that your daughter being 31, this is 13 years beyond the point she became an adult, thus very much time after the point when money could be claimed as child support, and 7 years beyond the end of the statute of limitations, as provided by the Limitation Act 1980. To answer your question regarding EU law, it only provides procedural help, i.e. easier access to the courts and enforcement authorities of the other EU states. What it does not provide is an extension of the statute of limitations, nor alternative causes for action. In other words, the first thing to do is to ask in the UK whether you can obtain a new order for him to pay the arrears in child support. The place to do this is the Child Maintenance Service / Child Support Agency (https://www.gov.uk/child-maintenance/overview).
If you do have a new court order (not the old one, because it has been covered by limitation as well), then as any money order you may more easily enforce it anywhere in the EU because it is automatically recognized, so what you would do is go directly to an Irish bailiff / sheriff with it for enforcement against the property. But if you cannot obtain a new court order, then I am afraid you cannot do much based on the documents that you already have.
Note that the CMS / CSA does have a number of non-financial sanctions for erring parents, such as applying to take away their drivers' licence. However, they do not affect those who are neither UK citizens nor residents, because these measures are restricted to UK soil. Thus someone living abroad, as long as they avoided the UK, would not feel their effect.
Going away around the world is a time-tested way of avoiding all kinds of obligations. In theory, when he moved to Malaysia, the law says you could have gone after him there with your UK court order and have an 'exequatur' (i.e. recognition and enforcement) of the UK court order there. The fact that it would probably have been too expensive / too much of a headache is the reason why most people do not do it, and why going away is still a doable means of avoiding paying child support.
To sum up, I recommend contacting the CMS / CSA for advice on whether you can obtain a new court order for the arrears. If you can, you are in luck and can go directly to the bailiff / sheriff in Ireland, because that would be a European Money Order, and could be enforced straight away.
Please do not forget to rate my answer.
Dr Ioan-Luca Vlad