Wow, this Military Spouse Residency Relief Act is a hot topic. There is so much information and the guidance that is coming down from the individual states is sketchy, at best.
One of the most popular questions is when a service member has residency in a certain state (let's say Florida) and the spouse was not originally from Florida, has never lived in Florida, and has been changing their driver's license and voter registration every time they move. The MRSSA states that the spouse can maintain their domicile (residency) in the same state as the active duty service member, but it doesn't tell how to obtain that domicile (residency) in the first place.
This article from Defense.gov makes it seem like the MSRRA has just opened up a whole new can of worms regarding residency. It states:
“One common misperception is that the new law allows a spouse simply to ‘choose’ his or her spouse’s domicile. This is not true,” he said. “Domicile must still be demonstrated or proven under the rules that have always been in place. Likewise, a spouse does not ‘inherit’ the domicile of the military member through marriage.”
Spouses also should be aware that the law doesn’t allow them to recapture or regain a previously abandoned domicile, he added.
This is pretty darn unhelpful, in my opinion. I could write a mile-long list of the problems with this set up, but I'm guessing that you have your own list. At this point, spouses appear to have two choices: stick with their current domicile, or make some questionably legal moves to establish their domicile in the home state of their service member. There are a few situations in which is should be pretty easy: if you are currently stationed in the state that the service member claims residency, then you should change all your stuff right now, while it is quick and unquestionable. If either set of parents live in the state, you may find it pretty simple to change your things over using the parents' address. (Legal, I'm not sure. Easy, probably.)
If you are living in a state that is not your spouses' domicile, and your parents don't live there, you may encounter some difficulty in establishing domicile there. The way I read the Defense.gov article, you don't have the right to claim your service member's domicile just because it is their domicile, you must have some other justification for claiming it. However, many states are providing guidance on how to establish domicile in their state. (See the state-by-state links.) It seems like this wasn't thought through very carefully when the law was written.
I know that this probably doesn't answer any of your questions, but hopefully it has provided a little bit more information. The group that helped push the MSRRA through Congress maintains a Facebook page and it is a good source of information. I promise that I'll keep you up to date as I learn more.