That's an interesting dilemma, because on the other hand how do you force her to stay in this country? She has a right to live wherever she wants. I wonder what precedence we have for this type of situation and what courts have ruled.
family courts can, and do, rule that parents cannot even move out of the same city. if she had no kids, she could do whatever she wanted with the alimony and live in whatever country she wanted. when minor children are involved, a custody agreement can stipulate that the parent with primary custody cannot move the children an x amount of distance away from the other parent. a custody agreement will take priority over her rights to live where ever she wants. if she moves anyway, she is in violation of the custody agreement and can lose custody of her children completely. ive read bits of court cases here where parents have lost custody because they violated that court order on custody. even when a job is involved and the "reason" for moving, it can be enforced.
not if a good lawyer, and a family court judge with half a brain and sensitivities that children need to be near their father, have their way.
the major wrench in these laws are that they have to be observed by the country the wife and kids move to. dont know how sweden handles it but it seems like most countries will support their citizens---even if the kids are not their biological kids. remember the nj dad trying to get his kid from the stepfather in brazil?
if she moves the kids there. some US judge can order the kids back or something but have no power to enforce it. im assuming she's a swedish citizen, but maybe not. she may have dual. anyway her parents are swedish and sometimes thats enough. the brazilian grandparents were the main ones fighting the nj dad from getting his son--although the big difference with that case was that the child had lived in brazil for a couple yrs with the biological mom before she died.
She can leave whenever she likes. The kids however will have to remain. She's both a Swedish and a US citizen.