With regard a legal document saying they have to stay with your wife, just bear in mind that if you wife is staying here, and you want to take the kids out of the country, to say Dubai (Wild Wadi) or on a Rugby Trip or to see the F1 or whatever and your wife is not going, they may not be to happy about you taking the children out of the country unless you have adopted them, or you have a legal notarised letter from your wife authorising you to take the child(ren).

May seem that it won't happen but consider an emergency where the wife flies back to UK, and you and child end up having to follow.