As a fellow milspouse RN, I will answer these questions the best I can:
Milspouse RNs can work wherever. Some work at the military hospital on post; others will work at on post clinics or off post at a hospital. Where I am stationed, it seems like the nearby Army hospital only took experienced RNs (with at least 2 years of experience) so I had to look for a job off post. I graduated in December 2010 with my BSN from a nursing program in Ohio. I kept working as a nurse tech until April because I knew in May I would be relocating with my husband to his duty station in Texas. I was so worried about finding a job because while I was still living in Ohio, I sent in a lot of job applications but didn't have any luck. Once I actually lived in Texas and started applying, I had more luck. I found a job within 2 weeks of living there. The hospitals off post (at least around here) are used to having nurses who are military spouses or who are in the military themselves, therefore people come and go. They were very accepting to the fact that I was a military spouse and although I didn't mention it, they knew I wouldn't be with the hospital for years. Military hospitals are the same way; they are used to employees coming and going because of deployments, orders to PCS, etc.
If you are looking for a job on post, whether it be in a military hospital, clinic or at the VA, check out usajobs.gov for vacancies. You will also be eligible for military spouse preference when applying for these jobs, as long as you meet the other requirements, too. You can also talk to people on post at centers in regards to finding a job. I plan on doing this for when I move because I know I will be PCSing with my husband to Missouri (or as we call it, to "Fort Lost-in-the-Woods, Misery") and my hospital choices in the area will be VERY limited. According to my husband, I could talk to these people about my qualifications and I could tell them I would be moving to Missouri in x amount of years so by then I would hopefully have a job. He said they would HAVE to find me a job. Talk to your hubby about this!
In regards to your license, I was actually speaking to my PCP at an appointment one day, who is affiliated with the hospital on post but provides care at the clinics on and off post. She is a nurse practitioner. She was telling me about the benefits of having a DOD nursing job. When talking about the license, she said with a DOD job they will accept any state license. For example, say I work in a military hospital/clinic with a TX nursing license, then I PCS to D.C. and work at the Walter Reed Army Medical Center, they should honor my TX nursing license.
If you are going to an OCONUS location, you could work at the on post hospital/clinic(s). I currently work with a few RNs who were stationed in Germany and they said they were able to find work, but those jobs were hard to come by. If you are already in the DOD system it might be easier for you to find a job should you PCS overseas but again, you aren't guaranteed a job. Remember those people you could talk to on post? This would be a great question to ask them. In fact, all of these questions would be great questions to ask them (sorry I am totally blanking on what these centers are called!)