Something doesn't add up here. Members of the US military stationed overseas or even in a different state on active duty do NOT lose their state residency status. That's why they're still entitled to vote by absentee ballot in elections in their declared state of residency.
That's my understanding, too. We have one side of the story here, short on details. Without names, dates or locations, it's all but impossible to check facts. Not to mention that there's another page, linked from the top of the page above, saying that the kids were back with their father in October and remained with him as of December 2nd. The version of the story so far is way heavy on outrage and light on facts.