Jim, you did ok mate under the circumstances. I think your starting to realize now how much this is effecting batgirl, and the impact it will have on you at this time. Batgirl will get better, trust me on that, but its going to be a long hard road to get her there.
Now whilst you did what you thought right at the time, I wouldn't go with the slapping when she gets hysterical in the future. Why? Whilst a slap will often ground a person again from hysterics, it is often something that is only used once or twice with a person. Batgirl is not going to get hysterical once or twice, trust me, its going to happen often in regard to anything military related, and its going to happen a lot more when she starts to really face her trauma.
My suggestion! I would go for the holding her real tight so she can't hurt you, your wife or anyone else, until she calms down from the moment. If you slapped her each time, eventually she will resent you for it because its a form of violence. Violence to batgirl is the evangalist of the world falling apart. Whilst she may take it this time, or another couple of times, she will run from it eventually.
ER... they can't do anything for her at those times that you or your wife cannot. Hold her, talk to her in order to try and bring her back. Ground her basically, back to reality and out of hysterics.
Batgirl will never get past the trigger of military, and I mean ever. Whilst with work she can become more tolerant of military aspects in small doses, if exposed for a constant short period, it will break her again. The reason is pretty simple, in that the military is the primary cause to her pain. Whilst trauma can be healed, the cause of it will never be fully accepted. Military comes with violence, and that is factual. The military is not a job that trys to talk their opposition to step aside, it uses violence, and so anything that stems military, to her equates to violence / possible violence against her.
Batgirl does understand that her father and brother are dead, she just doesn't want to accept it yet. She will as part of her trauma therapy, but she hasn't gotten that far just yet. People often use the very appropriate phrase "walking on eggshells" when dealing with someone with uncontrolled PTSD and trauma. Often spouses and family actually. This is what your going to feel like at times in regard to batgirl, and this is whats really essential at times unfortunately, until she heals some of her trauma. She has healed nothing as yet, instead her pain has only grown over the past five years, because instead of getting any of it out, she has kept it all in not knowing what to do with it, hence the pain is on a continuous growth cycle, along with her suffering.
Jim, all I can say mate at present, is brace yourself for one hell of a learning curve. Its going to get a lot worse before it gets better. At present, she is existing, not coping, not living, just existing... When she starts poking away at her trauma, she is going to be less than existing, instead she will be in constant suffering. Suffering will stem from having to face her past, face her greatest fears, face the reality of what was happened to her. I know that you may think she knows it, but she doesn't understand a single thing from what has happened yet, and that is whay she has to find, which is going to cause an extreme amount of pain for her, thus an extreme amount of suffering. As a result, those around her will also suffer her backlashes from trauma therapy. Its a painful process for everyone involved, it truly is.
The next step from existing, is suffering. The next step from suffering is death. Trauma therapy is going to push her boundaries into these regions, and it is a very dangerous area to be within. I think you can work out just how much pain she is going to endure in order to heal her past.
Jim, just remember mate, be kind to yourself during your supporting her, because whilst she may get very mad and angry at you, its not actually her true self fronting you or your wife, its her past coming through. You are both going to learn a whole new level of tolerance I believe. Don't be surprised at all if she runs at some point again. If she does, hopefully it won't be for long, nor permanent, just a temporary lapse to get herself some time and space from life.
Batgirl has suffered some of the worst life could throw her way... and unfortunately, she is going to throw some of that your and your wifes way as a result, atleast until she is healed somewhat. It takes a good year of hard work and pain to balance out, then another couple of years minimum to fine tune skills, learn techniques that work uniquely for the sufferer and so forth. Its going to be a long hard road mate... and even longer for batgirl, because she has physical limitations that will be provoked from her mental healing process.
Just please don't take anything she does personally towards you Jim, because she's over the moon mate that she has you both back in her life, she just has to find her feet now to no longer exist, but live.