I took the time to read the whole Convention.
Hopefully you read the associated child laws from Ireland which form part of this.
it is then up to the father to refute those facts.
No its up to her to prove facts, she abducted the children from their habitual residence. She is in the wrong.
to live in an unhealthy atmosphere or are likely to be in physical or mental danger
Our interpretation of this will be wildly different to a courts. The fact is that it is the state that protects the children and without doubt the Irish state can provide the care required for this family. It has to be said the opposite is true in Poland. This will not please a few on here.
If the children are returned to Ireland you have to consider where they will live and who will pay for this..
How did they survive before? The state will provide as they did before. The mother screwed up and has incurred a boat load of expense. It would have been far simpler to do it right in the first place. IE go to court and come to an agreement with the father and the courts. The courts often agree the children can go back to live in Poland, especially if the mother can be trusted. Now, she can hardly be considered good mother material.
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If only these Mothers/Fathers took sensible advice (not from their friends) before vanishing with the kids. Its not rocket science and if they live with an abusive partner, the courts would definitely take a positive view, whereas you disappear with kids and your the one looking incredibly bad. The most common excuse for not going through the court is, I didn't have time. You didn't have time, but you had time to plan it. You can get in a family court the same day in the UK.