There are currently no Minnesota cases directly on point to answer this question. One federal case that may be helpful is a 2013 case called Ozaltin v. Ozaltin, 708 F3d 355.
The Hague Convention is a possible resource as it has been signed by both Great Britain and the USA. The issue with the Hague Convention is that it deals more directly with the abduction of a child from the child’s habitual residence. The Hague Convention does not deal very effectively with the situation in this type of case where a court may allow a custodial parent to move and live in England. In cases like this, all the law provides is that the American State Department will help facilitate visitation. However, there is no enforcement mechanism.
After consulting with an English Solicitor in England on this subject, the Solicitor said that it was clear that since the children’s habitual residence would be England, that a court in England would assert jurisdiction over the children. The Solicitor recommended that if the parent is allowed to move to England with the children, the U.S. court should require that the parties obtain a ‘Consent Order’ in England before the parent is allowed to move with the children to England. This would require signatures but no court appearance in England by the parties. The solicitor recommended this so that the courts in England would know what terms to enforce regarding parenting time/visitation, who has to pay for travel visits, and any other issues that may arise.