I am inexperienced with legal aspects. I am 20, with a 4 year old son. I am going through a divorce and have done everything on my own so far. I have included in my agreement with my ex that I will be moving to be closer to a more supportive family, also. The ex does not currently live in the same state with me, so I am all alone if anything happens. I don't have anyone, and as a single mom, full time worker, and full time student, I do not have time to meet friends. So, I believe the move is the best I can do for my son. That is the bottom line.
Even when I was living with my ex, it was the same thing. No support at all. It can be very beneficial to have full custody. A perfect example of this is when him and I lived together, we had a baby sitter for my son. I picked up my son one afternoon with a huge gash over his left eye. I called his dad to tell him I was taking my son to the ER. My ex's response to this? "How big is it? Can't it wait 'till I get home? (in 4 hours)." My son got three stitches, he was crying and screaming, and my ex wasn't even there (he was off work alreay, I was in the ER for several hours). And the babysitter was his idea, because he wanted to "save" money. Fact of the matter is, I could have paid for a good daycare if I wasn't paying for his $520 car each month (which btw I don't have my name on).
Physical custody is good for having your son live with you, go to school with you, etc... Legal custody is where religion, education, and medical decisions come into play. Consult with a lawyer and see how to proceed, but if you know that this is best for your son, then do it.
Being a single mom needs is that much more challenging. I would think that as long as you have legitimate reasons for asking for this the judge would seriously consider it. I have custody of my children and I'm looking at moving no more than an hour away from him. I was concerned that Jerk would throw a fit over this (which he did) but his attorney pretty much told him it would be what it would be. My attorney told me that if I wanted to move across the state (7 hours) away and could show that I had a good reason, such as a great job offer, and that my children would have a secure home the judge would probably grant it. With your husband in the military it seems like his stability could be questionable giving you even more of a reason to go where there is stability. Not legal advice...only my opinion. Good luck.