You son sounds like mine. He has to be active and if he's not then he goes crazy and starts acting out.I am also a military wife,7 years, so I know what you are talking about with deployment and work up schedules. My kids also know all about deployments and work ups and TAD etc!!!
When my son was around 3.5 we moved to Ft. Bragg and the first thing I did was get him into the part day pre-school as well as gymnastics and soccer here on base. I don't know what branch you are but I'm sure there is a child and youth services of some kind that offers many different activities for little ones. Here on Bragg if your husband is deployed most of them are free all you have to do is register them. If he's not deployed then the part day pre-school is based on your husbands rank/income, the soccer was $26 for the entire season and that included his shirt, and gymnastics is only 30 or something like that a month. So I guess what I'm trying to get at is that it's not expensive and it gives him some sort of schedule and familiarity as was well as an outlet for energy!!! It gives him something to look forward to everyday and it also gives you a bargaining chip at the same time. All while allowing you to devote time to your work while he is at school during the day and not have to worry about neglecting him.
Another thing I do with my kids while daddy is gone is once a week my oldest(now 4.5) gets to pick a place to go eat dinner. It's usually chick-fil-a. We go there, the kids eat their dinner and go play in the play area for an hour or so, whatever I feel I can handle while just sitting there :) Then instead of opening their happy meal toys we turn them back in, get an ice cream, eat that and go home. Another cheap way to make him feel special since hes the big boy and gets to pick, he runs off energy while playing, and he has something once a week to look forward to.
I hope I didn't ramble too much and this helps. If you need anything else or just someone to talk to about deployment stress and kids please feel free to pm me...Good Luck