I work full time and board my horse at a full care facility. I also do day trips by plane twice a week, so even if I had the land to keep my horse at home, it would be difficult to care for him myself (and DH is already unhappy when he has to clean the litterbox while I'm gone on longer trips, so I doubt he'd be happy about mucking out a stall!)
I get out to ride 3-4 times per week usually (a covered, lighted arena is critical!). However, lately I've been really swamped at work and haven't had a chance to ride much (plus a week of vacation and a week at a conference) so I finally broke down and asked my trainer to ride him a few times. I don't have any kids, but I still find it difficult to balance work, home & horse life sometimes...
You have the added challenge of being a military spouse, which means that, if you buy, you'll have to consider the extra effort it will take to move your horse whenever you get a PCS.
Leasing could be an option for you, but has the downsides of you not getting to make as many decisions about the horse's care/training (usually less of an issue if you do a full lease), possibly having to 'start over' to some degree with every new horse you lease, and investing in tack/training/etc that doesn't carry over to future horse(s). There's no standard contract terms for leasing, so make sure you don't get locked in for a set time period since you have a high probability of moving (30 days notice is generally fair for both parties)