Where the country your children are living in has become their habitual residence, there are legally two ways in which you can relocate your children to another country; with the other parent's consent or with the consent of the court of the country your children live in. That court can carry out a full welfare assessment to decide whether the relocation is best for your children in the event of a dispute.
What if you relocate your children without the other parent's consent or that of the court? That is where the 1980 Hague Convention on the civil aspects of international child abduction applies. The purpose of the convention is child focused, it aims to return children who have been abducted by one parent back to their country of habitual residence so that the courts in that country can decide what is best for them as described above. The Convention therefore hopes to deter international parental child abduction and promote comity between international countries meaning that we should respect the laws and process of the countries who are signatories to the 1980 Hague Convention (now over 100 countries worldwide).
Court proceedings raised under the 1980 Hague Convention are purposely a summary process. What that means is that it is a very short court process where a full welfare assessment is not completed because that is not the purpose of the 1980 Hague Convention. The Hague convention considers decisions on a child's welfare are always best taken in the country in which the children are habitually resident.
There are defences available under the 1980 Hague Convention such as consent/acquiescence, children's views and that the return would place the children at grave risk of being returned to an intolerable situation. If there have been any allegations of abuse in any form whether those allegations are substantiated or not, the court will consider whether the country in which the children are being returned to can be trusted to put protective measures in place for the other parent and/or the children if necessary. What the court will also consider is the short-term situation on the ground when the children are returned and this will cover making sure that they have, in the short-term, adequate accommodation, access to income, whether that be via state benefits or employment (including legal aid), and access to healthcare. Fundamentally though, it's not for one country to substitute its legal system for that of another and appropriate deference to that other country should generally be given. Without such an agreement between countries there may be chaos with parents absconding to a country chosen for the most likely favourable outcome.
This is a highly specialised area and whether you are a parent who has had their children abducted from them or you are a parent who has removed children, obtaining immediate expert legal advice is critical to getting the best possible outcome.