The link has all the nitty-gritty. For those who want a short summary:
Military spouses are given hiring preference at DoD (military) facilities if they have relocated (PCSed) with their sponsor to a new duty station. You would be given hiring preference if you were a qualified candidate...that is, all other things were pretty much equal between you and other top candidates. You have to apply for it at the new duty station, you have to meet all of the qualifications, and it's a one-time use thing.
What it WON'T do:
* It does not guarantee you a job
* It does not mandate that they have to create a position for you, or tailor a current opening just for you
* If you lack experience or qualifications that the job needs, military spouse preference won't make up for them (i.e., it won't substitute for a specific degree, actual years RN experience, or specialty skills/certifications needed for the job)
* It does not mean they can't hire a non-military spouse applicant instead, especially if they were more qualified than you
In your case, I'm not sure it may be that helpful for you unless you applied for new grad level jobs. That being said, you have nothing to lose by registering for it and trying!
As far as civilian facilities go, there is no mandate AFAIK that they have to give military spouses preference. Some places do like to hire military spouses because they support the military. Others run far away from military spouse applicants because there is often high turnover from them (e.g., regular PCSing, or the spouse who only likes to work when their military member is deployed).
That link I provided also provides links to organizations that you should check out to help you in your search. The military is aware that life is hard on the spouse, so they provide a lot of career resources.
But remember that the military does not have to hand YOU a job nor kill themselves to get you one. There's an old saying: "If the military wanted you to have a family, they would have issued you one." I've been doing this spouse bit for 18 years, and while the military has grown more supportive of families during that time...at the core, that attitude remains the same :/
Best of luck.