Sure, But if the father files for divorce when you do this you can be made to move back or give up the child.

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If you move out of state without filing for divorce, the father may be able to compel your and/or the child's return.

The father of the children can of course file for custody and get a court order from the court that orders her to return to the state with the children.

So she just takes the risk of possible loss of custody if she did not do that or the trouble of moving back if so ordered. So they have to decide the risk.