Military spouse can claim a NEW state of residency once they have established residency in that state.  After that they can remain a legal resident of that state even if they move as long as they remain married to the military member.

In the situation you described I don't think the spouse can change their state of residency because they have not ESTABLISHED a new state of residency.

https://militarybenefits.info/military-spouse-act-residency-relief-msrra/