ROI? Is there a country called ROI? If so, I haven't come across it.
If you mean Ireland, as I assume you do, Ireland, like France or Spain or Italy is an EU Member State which is a signatory to the Hague Convention. Generally speaking, all Hague Convention countries will return children to their State of habitual residence if kidnapped there in breach of the Convention, but the process can be complicated and costly. The process necessarily involves the courts, the views of any Irish (or indeed other) Government at any point in time are entirely irrelevant.
It is worth noting that Ireland (unlike Germany) is a dualist system, and that Children's Rights are expressly protected by the Irish Constitution, so it is theoretically possible that Ireland could refuse to return Irish citizen children to the UK (in breach of the convention) if the Irish courts felt that the British courts wouldn't sufficiently vindicate the rights of those children. I just can't imagine a practical scenario where this might happen given the Convention. A German Court would have a far more difficult time ignoring the convention than an Irish court would, and there are significantly more Irish citizen children ordinarily resident in the UK than there are German citizen children.
I digress, my point was simply that most parents wanting to bring their children to their home country to visit their family want to bring their children on holiday to visit their family. They don't wish to kidnap them.
English law requires that the parent denying permission to travel have good reason to do so. If they don't have good reason a) the courts will rule against them and costs may be awarded against them b) they may hurt their kids by denying them a connection with part of their family and heritage c) their ex may frustrate their future foreign holiday plans which their ex needs to consent to in a tit for tat situation they started.
If the OP is genuinely concerned she should speak to a lawyer.
She shouldn't take advice on something this important from someone who doesn't even know that it's a court process, let alone that there's no country called ROI (and that the Irish courts will reject legal proceedings out of hand if they're addressed to "ROI" because it's not the name of the country).