I haven't read every post on this thread but the little that I have seen tells me you have a lot on your plate right now kdoelit. Moving is hard and your husband going away can be really tough in so many ways.
I don't know if has been mentioned but I would think if your son loved being in the backyard before then he has more excess energy to manage in an apartment. Is a small exercise trampoline feasible? Maybe not if you have neighbors below. It's not a solution to all your problems but extra energy needs an outlet. Too much undirected energy can make a child feel edgy and they can have difficulty controlling how it explodes. Sports, running around the park, swimming, anything might help. But, I get it might be hard if you have another child and a husband away to fit in some activities.
When my husband was away and our DD was young, and he was away a lot, she would get quite sad at this age. I was also really tired so it makes coping that much harder.
Kudos to you for reaching out and trying to find different solutions.
Are there any military backed programs you can access to help your son? Our military puts Defence liaison aids in schools with lots of military kids. They also have family support including social workers and booklets for kids explaining why dad or Mum is away etc. spouses also get funding for job search. I don't know what may be available to you.