Wow. I've seen this before, in my own life. I'm married to a veteran with PTSD. I think you are, too, although you haven't put a name to it yet. Investigate on line and pull up a list of symptoms, or grab some literature from family services on base and take a look. I'll bet that what you read will look mighty familiar.
In one of those quiet moments, you need to sit down and tell your husband what you see. Be factual about his behavior and honest about how it is making you feel and the impact it is having on his children (and it IS having an impact - even at this age, they are learning about how men and women should relate to one another by watching you two). Accept that when you tell him, he probably isn't going to smile at you and say, "Thanks, honey." You need to tell him anyway. Encourage him to go get help NOW. There are resources on base, although I can't tell you about those specifically, since my hubby's PTSD hit critical post-retirement, and he gets the services he needs through the VA. Other posters have given you specifics about where to go. And while the stigma is not as great as it once was, yes, getting help might affect his career. Not getting help could destroy his family. Which is more important?
Help includes counseling, possibly medication, and support groups. If you are part of a faith community, look for help and support there, too. My husband is part of a group that works with horses - equine therapy - and for all that he claims he doesn't see how it helps, it HAS helped. Horses are very sensitive, and if he's not managing himself well, they won't let him approach them. It's hard for him to hear from me that he's having a low-control day. But when a horse tells him, he accepts it and works on it.
One thing to be aware of - a person who is currently in a state of reaction to stress (anger, irritability, out-of-proportion behavior) has a very hard time seeing that it is his problem. Inside your husband's head when he is behaving irrationally, he believes that he is fine, and the rest of the world (including you) is the problem. Talk to him when he is not being reactive about how you can safely let him know when he's losing control. We use a code word. If he is in the middle of being reactive and it is beginning to feel dangerous, leave. I don't mean forever - I mean for that moment. "I'm going to take the girls to the park so you can decompress, honey." Or encourage him to do so. "It looks like you need to blow off some steam. Why don't you go for a run?"
Finding ways to de-stress is important. My husband de-stresses by baking. This is a wonderful/awful thing, because he makes fabulous sweets. :-) He's in school right now, and I think I gained 5 pounds during his last week of finals.
If you're currently changing commands, that will make getting consistent help a little harder, but please don't wait. Encourage your husband to ask for help, and if he won't, then you need to anyway. Find someone - a spouse support group, a chaplain, someone in the family support center - and arm yourself with what you need to know to keep you and your girls safe and sane while he grapples with his condition. And you should know - studies now support something I've known for several years - the spouses of military members who have PTSD also begin to exhibit symptoms if it's left untreated, because the stress of living with someone who is angry all the time and feels dangerous to us is that great. Pay attention to your own stress reactions, especially as the mother of toddlers. If your reactions are growing out of proportion to their shennanigans, or if you find yourself in tears because somebody moved the milk, get some help for you, too.
Courage, my dear - you CAN fight this. PM me here if you'd like to talk some more.